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AustraliaNSW
Stage 5.1-3

5.03 Polygon proofs

Worksheet
Polygon proofs
1

Find the value of x in the following diagrams, showing all working and reasoning:

a
b
c
d
e
f
Applications
2

Find the value of \angle ABC in the diagram shown, where ABFGHand BCDEFare regular pentagons.

Show all working and reasoning.

3

The given diagram shows a regular heptagon, with each side extended to form a star shape.

Find the exact value of \angle XYZ using only the points provided.

Show all working and reasoning.

4

Find the value of \angle SRA in the diagram shown.

Show all working and reasoning.

5

The given diagram shows a regular nonagon. The points P, Q, and R lie on a straight line.

Find the value of \angle SQR.

Show all working and reasoning.

6

A Penrose tiling is a pattern formed from two particular rhombuses. An example is shown:

By studying the diagrams above and below, state the size of the largest and smallest two angles in each pattern piece:

a
b
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Outcomes

MA5.2-14MG

calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar

MA5.3-16MG

proves triangles are similar, and uses formal geometric reasoning to establish properties of triangles and quadrilaterals

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