 AustraliaNSW
Stage 5.1-2

7.02 Further triangle proofs

Interactive practice questions

Consider the diagram. a

Why is $BE$BE parallel to $CD$CD?

$\angle ABE$ABE and $\angle ACD$ACD form a pair of equal corresponding angles.

A

$\angle ABE$ABE and $\angle ACD$ACD form a pair of supplementary cointerior angles.

B

$\angle ABE$ABE and $\angle ACD$ACD form a pair of equal alternate angles.

C

$\angle ABE$ABE and $\angle ACD$ACD form a pair of equal corresponding angles.

A

$\angle ABE$ABE and $\angle ACD$ACD form a pair of supplementary cointerior angles.

B

$\angle ABE$ABE and $\angle ACD$ACD form a pair of equal alternate angles.

C
b

Which angle is equal to $\angle BEA$BEA?

$\angle BEA=\editable{}$BEA=

c

How do we know that $\triangle ABE\simeq\triangle ACD$ABEACD?

Two right-angled triangles have the ratio of their hypotenuses equal to the ratio of another pair of matching sides

A

Two pairs of matching sides are in the same ratio and the included angles are equal

B

All pairs of matching sides are in the same ratio

C

All three pairs of corresponding angles are equal.

D

Two right-angled triangles have the ratio of their hypotenuses equal to the ratio of another pair of matching sides

A

Two pairs of matching sides are in the same ratio and the included angles are equal

B

All pairs of matching sides are in the same ratio

C

All three pairs of corresponding angles are equal.

D
d

What is the scale factor relating $\triangle ABE$ABE to $\triangle ACD$ACD?

e

Solve for the value of $f$f.

Easy
Approx 4 minutes

Consider $\triangle ABC$ABC and $\triangle PQR$PQR.

Consider the following diagram:

In the diagram, $QR\parallel ST$QRST.

Outcomes

MA5.2-14MG

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