Congruent Triangles

Recognise the criteria for the congruence of triangles and solve related problems.

PairsLevel 1Level 2Level 3Similar ShapesExam-StyleDescriptionHelpMore Geometry

This is level 1; Determining whether two triangles are congruent and finding the reason. The diagrams are not drawn to scale. Lengths and angles are not always shown in proportion.

For each pair of triangles select the correct description of congruency.

1.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

2.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

3.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

4.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

5.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

6.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

7.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

8.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

9.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent

10.

 A. SSS - three sides B. SAS - two sides and the included angle C. ASA or AAS - two angles and a corresponding side D. RHS - right angle, hypotenuse and another side E. Not (necessarily) congruent
Check

This is Congruent Triangles level 1. You can also try:
Level 2 Level 3

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Description of Levels

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Pairs - The classic pairs game with simple congruent shapes.

Level 1 - Determining whether two triangles are congruent and finding the reason

Level 2 - Further questions on recognising congruency ordered randomly

Level 3 - Use your knowledge of congruent triangles to find lengths and angles

Similar Shapes - Similarity is a related concept.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

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Curriculum Reference

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Quick Reference

The following conditions guarantee congruence:

SSS - Given the lengths of all three sides.

SAS - Given two sides and the included angle.

ASA or AAS - Given two angles and any side.

The following is a set of conditions that does not guarantee congruence:

ASS - Given two sides and an angle that is not included between them. However congruence could be confirmed if the angle is a right angle (RHS - right-angle, hypotenuse, side) or an obtuse angle or if the side not adjacent to the angle is longer than the side that is adjacent.

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