Cambridge International Mathematics

Assumed Knowledge (Geometry and graphs) 11

For example, these triangles are equiangular but clearly

triangleBis much larger than triangleA.

For example, trianglesCandDhave two equal sides and the

same non-included angle, but they arenotthe same triangle.

One and only one triangle can be drawn if we are given:

² two sides and theincludedangle between them

² one angle is a right angle, the hypotenuse, and one other side

² two angles and a side.

There are, however, four acceptable tests for thecongruenceof two triangles.

TESTS FOR TRIANGLE CONGRUENCE

Two triangles are congruent if one of the following is true:

² All corresponding sides are equal in length. (SSS)

² Two sides and theincludedangle are equal. (SAS)

² Two angles and a pair ofcorresponding sidesare

equal. (AAcorS)

² For right angled triangles, the hypotenuses and one

pair of sides are equal. (RHS)

The information we are given will help us decide which test to use to prove two triangles are congruent. The

diagrams in the following exercise are sketches only andare notdrawn to scale. However, the information

on them iscorrect.

80°

60° 40°

B

80°

60° 40°

A

C D

If we are given two sides and a non-included angle, more than one triangle can be drawn.

DEMO

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