Page 693 - Basic College Mathematics with Early Integers

Objectives 9.6 CONGRUENT AND SIMILAR TRIANGLES

Decide Whether Two Triangles
Are Congruent.
Objective Deciding Whether Two Triangles Are Congruent
Find the Ratio of Corresponding
Two triangles are congruent when they have the same shape and the same size. In
Sides in Similar Triangles.
congruent triangles, the measures of corresponding angles are equal and the lengths
Find Unknown Lengths of Sides of corresponding sides are equal.The following triangles are congruent:
in Similar Triangles. A D
3 in. 5 in. 3 in. 5 in.

B C E F
6 in. 6 in.
Since these triangles are congruent, the measures of corresponding angles are equal.
Angles with equal measure: ∠A and ∠D, ∠B and ∠E, ∠C and ∠F .Also, the
lengths of corresponding sides are equal.
Equal corresponding sides: AB and DE, BC and EF, CA and FD
Any one of the following may be used to determine whether two triangles are
congruent:

Congruent Triangles
Angle-Side-Angle (ASA)
If the measures of two angles of a triangle equal the measures of two angles of
another triangle, and the lengths of the sides between each pair of angles are
equal, the triangles are congruent.
A D

45 14 cm 45 14 cm

35 35
B C E F
For example, these two triangles are congruent by Angle-Side-Angle.
Side-Side-Side (SSS)
If the lengths of the three sides of a triangle equal the lengths of the corre-
sponding sides of another triangle, the triangles are congruent.
A D

7 m 8 m 7 m 8 m

B C E F
9 m 9 m
For example, these two triangles are congruent by Side-Side-Side.

Side-Angle-Side (SAS)
If the lengths of two sides of a triangle equal the lengths of corresponding sides
of another triangle, and the measures of the angles between each pair of sides
are equal, the triangles are congruent.
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B E
50 50
23 ft 23 ft
14 ft 14 ft

A D
C F
For example, these two triangles are congruent by Side-Angle-Side.
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