EXAMPLE 1 Identify congruent parts

Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.

SOLUTION

The diagram indicates that JKL TSR.

Corresponding sides JK TS, KL SR, LJ RT

Corresponding angles J T, ∠K S, L R

EXAMPLE 2 Use properties of congruent figures

In the diagram, DEFG SPQR.

Find the value of x.a.

b. Find the value of y.

SOLUTION

You know that FG QR.a.

FG = QR

12 = 2x – 4

16 = 2x

8 = x

EXAMPLE 2 Use properties of congruent figures

b. You know that ∠F Q.

m F = m Q

68o = (6y + x)o

68 = 6y + 8

10 = y

EXAMPLE 3 Show that figures are congruent

PAINTING

If you divide the wall into orange and blue sections along JK , will the sections of the wall be the same size and shape?Explain.

SOLUTION

From the diagram, A C and D B because all right angles are congruent. Also, by the Lines Perpendicular to a Transversal Theorem, AB DC .

Then, 1 4 and 2 3 by the Alternate Interior Angles Theorem. So, all pairs of corresponding angles are congruent.

EXAMPLE 3 Show that figures are congruent

The diagram shows AJ CK , KD JB , and DA BC . By the Reflexive Property, JK KJ . All corresponding parts are congruent, so AJKD CKJB.

GUIDED PRACTICE for Examples 1, 2, and 3

1. Identify all pairs of congruent corresponding parts.

SOLUTION

Corresponding sides: AB CD, BG DE, GH FE, HA FC

Corresponding angles: A C, B D, G E, H F.

In the diagram at the right, ABGH CDEF.

GUIDED PRACTICE for Examples 1, 2, and 3

In the diagram at the right, ABGH CDEF.

SOLUTION

2. Find the value of x and find m H.

(b) You know that H Fm H m F =105°

(a) You know that H F (4x+ 5)° = 105° 4x = 100 x = 25

GUIDED PRACTICE for Examples 1, 2, and 3

SOLUTION

In the diagram at the right, ABGH CDEF.

3. Show that PTS RTQ.

In the given diagram

PS QR, PT TR, ST TQ and

Similarly all angles are to each other, therefore all of the corresponding points of PTS are congruent to those of RTQ by the indicated markings, the Vertical Angle Theorem and the Alternate Interior Angle theorem.