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4-gons (Quadrilaterals)

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Understand 4-gons

Describe a quadrilateral using vertices, sides and non-crossing boundaries.

Topic: Quadrilateral Basics Skill: Define a 4-gon precisely

Classify 4-gons

Distinguish parallelograms, rectangles, rhombi, squares and trapeziums by properties.

Topic: Quadrilateral Basics Skill: Classify common quadrilaterals by properties

Prove opposite sides

Use triangle congruence or parallel-line facts to prove a parallelogram property.

Topic: Parallelogram Properties Skill: Prove opposite sides of a parallelogram are equal

Prove opposite angles

Justify equality of opposite angles using parallel-line angle relationships.

Topic: Parallelogram Properties Skill: Prove opposite angles of a parallelogram are equal

Prove diagonal bisection

Show each diagonal cuts the other into two equal parts.

Topic: Parallelogram Properties Skill: Prove diagonals of a parallelogram bisect each other

Identify by opposite sides

Apply a converse condition to prove a quadrilateral is a parallelogram.

Topic: Parallelogram Characterisations Skill: Use equal opposite sides to identify a parallelogram

Identify by diagonals

Prove a quadrilateral is a parallelogram from diagonal bisection.

Topic: Parallelogram Characterisations Skill: Use bisecting diagonals to identify a parallelogram

Understand midpoint theorem

Connect midpoints of two sides of a triangle with a segment parallel to the third side.

Topic: Midpoint Theorem Skill: State and explain the midpoint theorem

Prove midpoint theorem

Use congruence or parallelogram reasoning to justify the theorem.

Topic: Midpoint Theorem Skill: Prove the midpoint theorem

Use midpoint theorem

Find unknown side lengths and parallel relationships in triangles.

Topic: Midpoint Theorem Skill: Apply the midpoint theorem to find lengths

Prove midpoint converse

Show that a line through the midpoint parallel to a side bisects the other side.

Topic: Midpoint Theorem Skill: Prove the converse of the midpoint theorem

Prove medians meet

Understand why the three medians meet at one point.

Topic: Medians and Centroid Skill: Prove medians of a triangle are concurrent

Use centroid ratio

Find segment lengths when medians are divided in the ratio 2:1.

Topic: Medians and Centroid Skill: Apply the 2:1 median division property

Join midpoints of a 4-gon

Show that the quadrilateral formed by side midpoints is always a parallelogram.

Topic: Midpoint Quadrilaterals Skill: Prove midpoint quadrilateral is a parallelogram

Find missing parallelogram vertex

Use midpoint or diagonal bisection ideas to determine unknown coordinates.

Topic: Coordinate Applications Skill: Find the fourth vertex of a parallelogram using coordinates

Use coordinates with midpoints

Apply midpoint formula to verify quadrilateral properties.

Topic: Coordinate Applications Skill: Use midpoint coordinates in quadrilateral problems

Find reflection symmetry

Identify mirror lines in special quadrilaterals.

Topic: Symmetry of 4-gons Skill: Recognise reflection symmetry in quadrilaterals

Find rotational symmetry

Describe turns that map a quadrilateral onto itself.

Topic: Symmetry of 4-gons Skill: Recognise rotational symmetry and central symmetry

Tile with 4-gons

Use angle and side arrangements to understand quadrilateral tiling.

Topic: Tiling and Patterns Skill: Explain how any quadrilateral can tile a plane

Ask converse questions

Practice turning a theorem into its converse and testing whether it is true.

Topic: Logical Inquiry Skill: Form converses of quadrilateral theorems

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