 Middle Years

# 7.04 Congruent triangle problems

Worksheet
Corresponding sides and angles
1

It is known that \triangle PQR \equiv \triangle STU.

State the three pairs of equal sides.

2

It is known that \triangle CDE \equiv \triangle LMN.

State the three pairs of equal angles.

3

It is known that \triangle GHI \equiv \triangle LMN.

State the three pairs of equal sides.

4

It is known that \triangle STU \equiv \triangle ABC.

State the three pairs of equal sides.

5

It is known that \triangle PQR \equiv \triangle ABC.

State the three pairs of equal angles.

6

It is known that \triangle STU \equiv \triangle PQR.

a

State the three pairs of equal sides.

b

State the three pairs of equal angles.

7

It is given that the triangles \triangle ABC and \triangle DEF are congruent.

a

State the three pairs of equal sides.

b

State the three pairs of equal angles.

8

It is known that \triangle QPO \equiv \triangle CBA.

Find the angle of \triangle QPO that corresponds to the following angles of \triangle CBA:

a
\angle ABC
b
\angle BCA
9

It is known that \triangle BAC \equiv \triangle FED.

Find the angle of \triangle FED that corresponds to the following angles of \triangle BAC:

a
\angle ABC
b
\angle CAB
10

a

Find the triangle congruent to \triangle EAB.

b

Find the angle that corresponds to:

i
\angle EBA
ii
\angle BEA
c

Find the side that corresponds to:

i
AB
ii
AE
Unknown sides and angles
11

Find the value of the pronumeral in the following pairs of congruent triangles:

a
b
c
d
12

Given that the following two triangles are congruent, find the length of NM.

13

Given that the following two triangles are congruent, find the length of SU.

14

Given that the following two triangles are congruent, find the size of \angle DEF.

15

Given that the given two triangles are congruent, find the size of the angle \angle NLM.

16

Given that the given two triangles are congruent, find the length of the side SU.

17

Consider the following triangles:

Given that LM = ST, and \angle LMK = 79 \degree, find the value of x.

18

Consider the following triangles:

Given that AB = ST, and \angle UST = 48 \degree, find the value of y.

19

Consider the following triangles:

Given that EF = HJ, and EG = 7, find the value of m.

20

Consider the diagram:

a

State the test that proves triangles \triangle DEG and \triangle FEG are congruent.

b

Find the value of q.

21

Consider the diagram where AD and AC are straight lines:

a

State the test that proves triangles \triangle ACE and \triangle ADB are congruent.

b

Find the value of p.

22

Consider the diagram where PT and RT are straight lines:

a

State the test that proves triangles \triangle PTS and \triangle RTU are congruent.

b

Find the value of x.

23

Consider the diagram where JL and KN are straight lines:

a

State the test that proves triangles \triangle JKN and \triangle MKL are congruent.

b

Find the value of y.