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Angles with parallel lines

CONCEPTUAL
MathematicsGeometry|Ages 12—14|ID: mt_H_pNJ3ZI_S

Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles

Mastery Evidence

  • Identify alternate, corresponding, and co-interior angle pairs in a diagram with parallel lines
  • Explain why alternate angles are equal using the concept of translation along the transversal
  • Find missing angles in a parallel-line diagram using a combination of angle relationships

Assessment Prompt

“If [child] sees a Z-shape or F-shape formed by two parallel lines and a crossing line in a diagram, can they identify the equal angles and explain why they’re equal?”

Curriculum Standards2 alignments

8.G.5Common Core State Standards for Mathematics
Angle arguments and similarity

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

G
KS3.Maths.Geo.11The national curriculum in England
Parallel Lines and Angles

understand and use the relationship between parallel lines and alternate and corresponding angles

Mathematics · Key Stage 3

Prerequisites1

Show full prerequisite tree
  • Understanding angles (age 11+) hard

    Parallel line angles build on basic angle properties at points and lines

    • Angle Sum Rules hard

      Builds on KS2 knowledge that angles at a point sum to 360° and on a line to 180°

      • Types of angles (age 8+) hard

        Angle sum rules (360° at a point, 180° on a line) are applied through reading angle diagrams with correct notation

      • Degrees and turns hard

        Angle facts (at a point = 360°) require degree system knowledge

        • What Is an Angle? hard

          Degree measurement system requires understanding what an angle is

          • Types of angles hard

            Angle definition builds on understanding right angles

            • Right Angles & Turns hard

              Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse

              • Understanding angles hard

                Identifying right angles requires understanding what an angle is

                • 2-D shapes (age 6+) soft

                  Understanding angles as shape properties requires knowing basic shape properties

                  • Angles in triangles (age 6+) soft

                    Understanding defining attributes supports describing shape properties formally

                    • 2-D shapes hard

                      Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

                    • 3-D shapes (age 5+) hard

                      Identifying defining attributes builds on informal analysis and comparison of shapes

                      • 2-D shapes hard

                        Analysing and comparing shapes requires being able to name them first

                      • 3-D shapes hard

                        Analysing 3-D shapes requires recognising and naming them

                  • 2-D shapes hard

                    Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                  • 3-D shapes (age 5+) hard

                    Formal property description extends informal analysis of sides and vertices

                    • 2-D shapes hard

                      Analysing and comparing shapes requires being able to name them first

                    • 3-D shapes hard

                      Analysing 3-D shapes requires recognising and naming them

                • Position, direction, and movement hard

                  Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

                  • Positional Language hard

                    Position/direction vocabulary with right angles extends basic positional language

                  • Turns & Directions hard

                    Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                    • What Is a Half? soft

                      Understanding half and quarter turns benefits from the concept of halves and quarters

                    • Positional Language hard

                      Describing movement and turns builds on positional language

              • Types of angles (age 8+) soft

                Identifying right angles and turns is supported by the convention of marking right angles with a small square

              • Position, direction, and movement hard

                Right angles as quarter turns extends Y2 turn vocabulary

          • Right Angles & Turns hard

            Angle definition builds on classifying acute/obtuse angles

            • Understanding angles hard

              Identifying right angles requires understanding what an angle is

              • 2-D shapes (age 6+) soft

                Understanding angles as shape properties requires knowing basic shape properties

                • Angles in triangles (age 6+) soft

                  Understanding defining attributes supports describing shape properties formally

                  • 2-D shapes hard

                    Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

                  • 3-D shapes (age 5+) hard

                    Identifying defining attributes builds on informal analysis and comparison of shapes

                    • 2-D shapes hard

                      Analysing and comparing shapes requires being able to name them first

                    • 3-D shapes hard

                      Analysing 3-D shapes requires recognising and naming them

                • 2-D shapes hard

                  Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                • 3-D shapes (age 5+) hard

                  Formal property description extends informal analysis of sides and vertices

                  • 2-D shapes hard

                    Analysing and comparing shapes requires being able to name them first

                  • 3-D shapes hard

                    Analysing 3-D shapes requires recognising and naming them

              • Position, direction, and movement hard

                Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

            • Types of angles (age 8+) soft

              Identifying right angles and turns is supported by the convention of marking right angles with a small square

            • Position, direction, and movement hard

              Right angles as quarter turns extends Y2 turn vocabulary

              • Positional Language hard

                Position/direction vocabulary with right angles extends basic positional language

              • Turns & Directions hard

                Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

    • Understanding angles (age 10+) hard

      KS3 angle facts extend KS2 angles at a point, on a line, and vertically opposite

      • Measuring angles (age 9+) hard

        Finding missing angles extends Y5 additive angle reasoning

        • Measuring angles hard

          Must measure angles before solving unknown angle problems

          • Types of angles (age 8+) hard

            Measuring and drawing angles with a protractor requires knowing how to mark and label angles using standard notation

          • Degrees and turns hard

            Using a protractor requires understanding degree measurement

            • What Is an Angle? hard

              Degree measurement system requires understanding what an angle is

              • Types of angles hard

                Angle definition builds on understanding right angles

                • Right Angles & Turns hard

                  Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse

                  • Understanding angles hard

                    Identifying right angles requires understanding what an angle is

                    • 2-D shapes (age 6+) soft

                      Understanding angles as shape properties requires knowing basic shape properties

                      • Angles in triangles (age 6+) soft

                        Understanding defining attributes supports describing shape properties formally

                      • 2-D shapes hard

                        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                      • 3-D shapes (age 5+) hard

                        Formal property description extends informal analysis of sides and vertices

                    • Position, direction, and movement hard

                      Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

                      • Positional Language hard

                        Position/direction vocabulary with right angles extends basic positional language

                      • Turns & Directions hard

                        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                  • Types of angles (age 8+) soft

                    Identifying right angles and turns is supported by the convention of marking right angles with a small square

                  • Position, direction, and movement hard

                    Right angles as quarter turns extends Y2 turn vocabulary

                    • Positional Language hard

                      Position/direction vocabulary with right angles extends basic positional language

                    • Turns & Directions hard

                      Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                      • What Is a Half? soft

                        Understanding half and quarter turns benefits from the concept of halves and quarters

                      • Positional Language hard

                        Describing movement and turns builds on positional language

              • Right Angles & Turns hard

                Angle definition builds on classifying acute/obtuse angles

                • Understanding angles hard

                  Identifying right angles requires understanding what an angle is

                  • 2-D shapes (age 6+) soft

                    Understanding angles as shape properties requires knowing basic shape properties

                    • Angles in triangles (age 6+) soft

                      Understanding defining attributes supports describing shape properties formally

                      • 2-D shapes hard

                        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

                      • 3-D shapes (age 5+) hard

                        Identifying defining attributes builds on informal analysis and comparison of shapes

                    • 2-D shapes hard

                      Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                    • 3-D shapes (age 5+) hard

                      Formal property description extends informal analysis of sides and vertices

                      • 2-D shapes hard

                        Analysing and comparing shapes requires being able to name them first

                      • 3-D shapes hard

                        Analysing 3-D shapes requires recognising and naming them

                  • Position, direction, and movement hard

                    Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

                    • Positional Language hard

                      Position/direction vocabulary with right angles extends basic positional language

                    • Turns & Directions hard

                      Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                      • What Is a Half? soft

                        Understanding half and quarter turns benefits from the concept of halves and quarters

                      • Positional Language hard

                        Describing movement and turns builds on positional language

                • Types of angles (age 8+) soft

                  Identifying right angles and turns is supported by the convention of marking right angles with a small square

                • Position, direction, and movement hard

                  Right angles as quarter turns extends Y2 turn vocabulary

                  • Positional Language hard

                    Position/direction vocabulary with right angles extends basic positional language

                  • Turns & Directions hard

                    Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                    • What Is a Half? soft

                      Understanding half and quarter turns benefits from the concept of halves and quarters

                    • Positional Language hard

                      Describing movement and turns builds on positional language

        • Types of angles (age 8+) hard

          Finding unknown angles using equations requires reading angle diagrams and interpreting arc marks and notation

        • Angle Sum Rules hard

          Must know angle facts (360°, 180°) to solve unknown angle problems

          • Types of angles (age 8+) hard

            Angle sum rules (360° at a point, 180° on a line) are applied through reading angle diagrams with correct notation

          • Degrees and turns hard

            Angle facts (at a point = 360°) require degree system knowledge

            • What Is an Angle? hard

              Degree measurement system requires understanding what an angle is

              • Types of angles hard

                Angle definition builds on understanding right angles

                • Right Angles & Turns hard

                  Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse

                  • Understanding angles hard

                    Identifying right angles requires understanding what an angle is

                    • 2-D shapes (age 6+) soft

                      Understanding angles as shape properties requires knowing basic shape properties

                      • Angles in triangles (age 6+) soft

                        Understanding defining attributes supports describing shape properties formally

                      • 2-D shapes hard

                        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                      • 3-D shapes (age 5+) hard

                        Formal property description extends informal analysis of sides and vertices

                    • Position, direction, and movement hard

                      Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

                      • Positional Language hard

                        Position/direction vocabulary with right angles extends basic positional language

                      • Turns & Directions hard

                        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                  • Types of angles (age 8+) soft

                    Identifying right angles and turns is supported by the convention of marking right angles with a small square

                  • Position, direction, and movement hard

                    Right angles as quarter turns extends Y2 turn vocabulary

                    • Positional Language hard

                      Position/direction vocabulary with right angles extends basic positional language

                    • Turns & Directions hard

                      Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                      • What Is a Half? soft

                        Understanding half and quarter turns benefits from the concept of halves and quarters

                      • Positional Language hard

                        Describing movement and turns builds on positional language

              • Right Angles & Turns hard

                Angle definition builds on classifying acute/obtuse angles

                • Understanding angles hard

                  Identifying right angles requires understanding what an angle is

                  • 2-D shapes (age 6+) soft

                    Understanding angles as shape properties requires knowing basic shape properties

                    • Angles in triangles (age 6+) soft

                      Understanding defining attributes supports describing shape properties formally

                      • 2-D shapes hard

                        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

                      • 3-D shapes (age 5+) hard

                        Identifying defining attributes builds on informal analysis and comparison of shapes

                    • 2-D shapes hard

                      Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                    • 3-D shapes (age 5+) hard

                      Formal property description extends informal analysis of sides and vertices

                      • 2-D shapes hard

                        Analysing and comparing shapes requires being able to name them first

                      • 3-D shapes hard

                        Analysing 3-D shapes requires recognising and naming them

                  • Position, direction, and movement hard

                    Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

                    • Positional Language hard

                      Position/direction vocabulary with right angles extends basic positional language

                    • Turns & Directions hard

                      Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                      • What Is a Half? soft

                        Understanding half and quarter turns benefits from the concept of halves and quarters

                      • Positional Language hard

                        Describing movement and turns builds on positional language

                • Types of angles (age 8+) soft

                  Identifying right angles and turns is supported by the convention of marking right angles with a small square

                • Position, direction, and movement hard

                  Right angles as quarter turns extends Y2 turn vocabulary

                  • Positional Language hard

                    Position/direction vocabulary with right angles extends basic positional language

                  • Turns & Directions hard

                    Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                    • What Is a Half? soft

                      Understanding half and quarter turns benefits from the concept of halves and quarters

                    • Positional Language hard

                      Describing movement and turns builds on positional language

      • Types of angles (age 8+) hard

        Angles at a point, on a straight line, and vertically opposite are identified through reading standard diagram notation

      • Angle Sum Rules hard

        Point/straight-line/vertically-opposite angle rules build on Y5 angle-sum knowledge

        • Types of angles (age 8+) hard

          Angle sum rules (360° at a point, 180° on a line) are applied through reading angle diagrams with correct notation

        • Degrees and turns hard

          Angle facts (at a point = 360°) require degree system knowledge

          • What Is an Angle? hard

            Degree measurement system requires understanding what an angle is

            • Types of angles hard

              Angle definition builds on understanding right angles

              • Right Angles & Turns hard

                Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse

                • Understanding angles hard

                  Identifying right angles requires understanding what an angle is

                  • 2-D shapes (age 6+) soft

                    Understanding angles as shape properties requires knowing basic shape properties

                    • Angles in triangles (age 6+) soft

                      Understanding defining attributes supports describing shape properties formally

                      • 2-D shapes hard

                        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

                      • 3-D shapes (age 5+) hard

                        Identifying defining attributes builds on informal analysis and comparison of shapes

                    • 2-D shapes hard

                      Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                    • 3-D shapes (age 5+) hard

                      Formal property description extends informal analysis of sides and vertices

                      • 2-D shapes hard

                        Analysing and comparing shapes requires being able to name them first

                      • 3-D shapes hard

                        Analysing 3-D shapes requires recognising and naming them

                  • Position, direction, and movement hard

                    Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

                    • Positional Language hard

                      Position/direction vocabulary with right angles extends basic positional language

                    • Turns & Directions hard

                      Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                      • What Is a Half? soft

                        Understanding half and quarter turns benefits from the concept of halves and quarters

                      • Positional Language hard

                        Describing movement and turns builds on positional language

                • Types of angles (age 8+) soft

                  Identifying right angles and turns is supported by the convention of marking right angles with a small square

                • Position, direction, and movement hard

                  Right angles as quarter turns extends Y2 turn vocabulary

                  • Positional Language hard

                    Position/direction vocabulary with right angles extends basic positional language

                  • Turns & Directions hard

                    Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                    • What Is a Half? soft

                      Understanding half and quarter turns benefits from the concept of halves and quarters

                    • Positional Language hard

                      Describing movement and turns builds on positional language

            • Right Angles & Turns hard

              Angle definition builds on classifying acute/obtuse angles

              • Understanding angles hard

                Identifying right angles requires understanding what an angle is

                • 2-D shapes (age 6+) soft

                  Understanding angles as shape properties requires knowing basic shape properties

                  • Angles in triangles (age 6+) soft

                    Understanding defining attributes supports describing shape properties formally

                    • 2-D shapes hard

                      Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first

                    • 3-D shapes (age 5+) hard

                      Identifying defining attributes builds on informal analysis and comparison of shapes

                      • 2-D shapes hard

                        Analysing and comparing shapes requires being able to name them first

                      • 3-D shapes hard

                        Analysing 3-D shapes requires recognising and naming them

                  • 2-D shapes hard

                    Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first

                  • 3-D shapes (age 5+) hard

                    Formal property description extends informal analysis of sides and vertices

                    • 2-D shapes hard

                      Analysing and comparing shapes requires being able to name them first

                    • 3-D shapes hard

                      Analysing 3-D shapes requires recognising and naming them

                • Position, direction, and movement hard

                  Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns

                  • Positional Language hard

                    Position/direction vocabulary with right angles extends basic positional language

                  • Turns & Directions hard

                    Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1

                    • What Is a Half? soft

                      Understanding half and quarter turns benefits from the concept of halves and quarters

                    • Positional Language hard

                      Describing movement and turns builds on positional language

              • Types of angles (age 8+) soft

                Identifying right angles and turns is supported by the convention of marking right angles with a small square

              • Position, direction, and movement hard

                Right angles as quarter turns extends Y2 turn vocabulary

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