1. 4.2 – Congruent Figures
Geometry
Ms. Rinaldi

2. Congruent Figures
Two geometric figures are congruent if they have exactly the same size and shape.
Congruent Not Congruent
Same size and shape Different sizes or shapes

3. Congruent Figures
In two congruent figures, all the parts of one figure are congruent to the corresponding parts of the other figure.
In congruent polygons, this means that the corresponding sides and the corresponding angles are congruent.

4. Congruence Statements
When you write a congruence statement for two polygons, always list the corresponding vertices in the same order.
You can write congruence statements in more than one way. Two possible congruence statements for the triangles are:
Now you try…Write a different congruence statement for the triangles:

5. 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

6. Identify congruent parts
EXAMPLE 2
Identify congruent parts
Now you try…
Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.
Congruence Statement:
Corresponding Angles:
Corresponding Sides:

7. EXAMPLE 3
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

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

9. Use properties of congruent figures
EXAMPLE 4
Use properties of congruent figures
Now you try…
In the diagram at the right, ABGH CDEF.
Find the value of x and find m H.
Step 1: Which angle corresponds with angle H?
Step 2: You then know that
4x + 5 =_______
Step 3: Solve for x. x = _____
Step 4: Plug in x to find