1. 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 angles
J T, ∠ K S, L R
Corresponding sides
JK TS, KL SR, LJ RT

2. EXAMPLE 2
Use properties of congruent figures
In the diagram, DEFG SPQR.
Find the value of x.
Find the value of y.
SOLUTION
You know that FG QR. FG
= QR 12
= 2x – 4 16
= 2x 8
= x

3. Use properties of congruent figures
EXAMPLE 2
Use properties of congruent figures
You know that ∠ F Q.
m F
= m Q 68 o
= (6y + x) 68
= 6y + 8 10
= y

4. 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 .

5. EXAMPLE 3
Show that figures are congruent
Then, and by the Alternate Interior Angles Theorem. So, all pairs of corresponding angles 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.

6. GUIDED PRACTICE
for Examples 1, 2, and 3
In the diagram at the right, ABGH CDEF.
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.

7. GUIDED PRACTICE
for Examples 1, 2, and 3
In the diagram at the right, ABGH CDEF. 2.
Find the value of x and find m H.
SOLUTION
(a)
You know that H F
(4x+ 5)° = 105°
4x = 100
x = 25
(b)
You know that H F
m H m F =105°

8. GUIDED PRACTICE
for Examples 1, 2, and 3
In the diagram at the right, ABGH CDEF. 3.
Show that PTS RTQ.
SOLUTION
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.