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AustraliaNSW
Stage 5.1-2

7.01 Proving triangles congruent and similar

Worksheet
Congruent triangle proofs
1

Complete the following proof to show that \triangle KLN and \triangle MNL are congruent:

\text{ } \\ \begin{array}{cll} ⬚ \text{ is common} & \\ KL = MN &\text{(⬚)} \\ \angle KLN = ⬚ &\text{ (Alternate angles in parallel lines)} \\ \triangle NKL \equiv \triangle LMN &\text{(⬚)} \end{array}
2

Prove that the following pairs of triangles are congruent:

a

\triangle PQR and \triangle STR

b

\triangle ABD and \triangle CBD

c

\triangle DEC and \triangle FEG

d

\triangle ACD and \triangle ACB

e

\triangle PFG and \triangle PYX

f

\triangle PQX and \triangle RQX

g

\triangle WXZ and \triangle YXZ

Given XZ bisects \angle WZY.

h

\triangle WBY and \triangle ZAX

Given XZ= WY.

Similar triangle proofs
3

Complete the following proof to show that \triangle AXB and \triangle CXD are similar:

\text{ } \\ \begin{array}{cll} \angle AXB = ⬚ &\text{(Vertically opposite angles)} \\ ⬚ = \angle XAB &\text{ (⬚)} \\ \triangle DEC ||| \triangle ABC &\text{(⬚)} \end{array}
4

Prove that the following pairs of triangles are similar:

a

\triangle PQR and \triangle ABC

b

\triangle CDE and \triangle LMN

c

\triangle ZYC and \triangle ZXB

d

\triangle JKL and \triangle MNJ

e

\triangle JMN and \triangle JKL

f

\triangle ADE and \triangle ABC

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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

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