 AustraliaNSW
Stage 5.1-2

7.02 Further triangle proofs

Worksheet
Further proofs for similar triangles
1

Consider the diagram.

a

How do we know BE is parallel to CD?

b

Which angle is equal to \angle BEA?

c

How do we know \triangle ABE \sim \triangle ACD?

d

State the enlargement factor going from the smaller triangle to the larger triangle.

e

Find the value of the pronumeral.

2

Consider \triangle ABC and \triangle PQR:

a

Prove that \triangle ABC is similar to \triangle PQR.

b

Find the value of x.

c

Find the value of y.

3

Consider the following diagram:

a

Prove that\triangle AOB and \triangle DOC are similar.

b

Hence, show that AB \parallel CD.

4

In the diagram, QR \parallel ST.

a

Show that \triangle PQR is similar to \triangle PST.

b

Find the scale factor of enlargement.

c

Find the value of f.

5

Consider the diagram below.

a

Prove that the \triangle ABE and \triangle ACD are similar.

b

Find the value of f.

6

Consider the following diagram:

a

Prove that \triangle ABC and \triangle ADB are similar.

b

Find the length x.

7

Consider the diagram below:

a

Prove that \triangle ABE is similar to \triangle BCD.

b

Prove that \triangle EDB is similar to \triangle BCD.

c

Can we conclude that \triangle ABE is similar to \triangle EDB?

8

In the diagram, \triangle ABC is a right-angled triangle with the right angle at C. The midpoint of AB is M and MP is perpendicular to AC.

a

Prove that \triangle AMP is similar to \triangle ABC.

b

Find the ratio of AP to AC.

9

Prove that AB is parallel to CD for the following diagram:

10

Prove that CE = EB for the following diagram:

11

Prove that BD^{2} = AD \times DC for the following diagram: