Basic Mathematics for College Students

 

We can show that the triangles shown below are congruent by the SSS property:

9.5 Congruent Triangles and Similar Triangles 755

Self Check 1

Refer to the figure below, where

.

a.Name the six congruent

corresponding parts of the

triangles.

b.Find.

c.Find .m(FE)

m(C)

ABC  EDF

Corresponding parts of congruent triangles are congruent. Therefore, the

congruent corresponding angles are

The congruent corresponding sides are

b.From the figure, we see that. Since , it follows that
.
c.From the figure, we see that inches. Since , it follows
that inches.m(XZ) 11

m(PR) 11 XZ  PR

m(P)27°

m(X)27° X  P

YZ  QR XZ  PR XY  PQ

X  P Y  Q Z  R

X 4 P Y 4 Q Z 4 R

XYZ  PQR

Now TryProblem 33

D

C F

AB E

3 ft 7 ft^20 °

110 °

2 Use congruence properties to prove

that two triangles are congruent.

Sometimes it is possible to conclude that two triangles are congruent without having
to show that three pairs of corresponding angles are congruent and three pairs of
corresponding sides are congruent. To do so, we apply one of the following properties.

SSS Property

If three sides of one triangle are congruent to three sides of a second triangle,

the triangles are congruent.

CERT

S

D

34

5

(^53)
4
Since and , the segments are congruent.
Since and , the segments are congruent.
Since and , the segments are congruent.
Therefore,CDE  STR.
EC  RS m(EC) 5 m(RS) 5
DE  TR m(DE) 4 m(TR) 4
CD  ST m(CD) 3 m(ST) 3
StrategyWe will establish the correspondence between the vertices of
and the vertices of.
WHYThis will, in turn, establish a correspondence between the congruent
corresponding angles and sides of the triangles.
Solution
a.The correspondence between the vertices is

PQR

XYZ

SAS Property

If two sides and the angle between them in one triangle are congruent,

respectively, to two sides and the angle between them in a second triangle, the

triangles are congruent.