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iGCSE (2021 Edition)

10.02 Congruent triangle tests (Extended)

Worksheet
Triangle congruence tests
1

For each pair of triangles, state whether the two triangles are congruent. If yes, state what congruence test they satisfy.

a
b
c
d
e
f
g
h
i
j
2

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test this pair satisfies.

3

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

4

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

5

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

6

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

7

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

8

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

9

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

10

Consider the following triangles:

Triangle A

Triangle C

Triangle B

Triangle D

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

11

Consider the given diagram:

State the congruence test that triangles \triangle ABD and \triangle CDB satisfy.

12

Consider the given diagram:

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

13

Consider the given diagram where KMand LN are straight line segments:

a

State which two triangles are congruent.

b

State the congruence test that this pair satisfies.

14

Consider the given diagram:

a

State which two triangles that are congruent.

b

State the congruence test that this pair satisfies.

15

Consider the given diagram:

What information is needed so that the triangles \triangle PQR and \triangle PSR are congruent?

16

Consider the given diagram:

What information is needed so that the triangles \triangle JKN and \triangle MLN are congruent?

17

Consider the given diagram where X is the centre of the circle.

What information is needed so that the triangles \triangle PQX and \triangle RSX are congruent?

18

Consider the given diagram:

a

State the congruence test that triangles \triangle EFG and \triangle EHD satisfy.

b

State the three ways in which the triangles satisfy this congruence test.

19

Consider the given diagram where X is the centre of both circles:

a

State the congruence test that triangles \triangle ABX and \triangle DCX satisfy.

b

State the three ways in which the triangles satisfy this congruence test.

20

Consider the given diagram:

a

State the congruence test that triangles \triangle ABD and \triangle CDB satisfy.

b

State the three ways in which the triangles satisfy this congruence test.

21

Consider the given diagram:

a

State the congruence test that triangles \triangle ABX and \triangle DCX satisfy.

b

State the three ways in which the triangles satisfy this congruence test.

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Outcomes

0580E4.1

Use and interpret the geometrical terms: point, line, parallel, bearing, right angle, acute, obtuse and reflex angles, perpendicular, similarity and congruence. Use and interpret vocabulary of triangles, quadrilaterals, circles, polygons and simple solid figures including nets.

0580E4.5

Use the basic congruence criteria for triangles (SSS, ASA, SAS, RHS).

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