Geometry – Unit 5 Triangle Congruence
Day 1
Warm Up
The variable expressions represent the angle measures of a triangle. Find the
measure of each angle. Then classify the triangle by its angles.
1.
mA  x 
mA  (x  22)
mB  (x  16)
mC  (2x  14)
2.
mB  (4x)
mC  (5x)
Find the value of x.
3.
24 in.
(6x + 12) in.
4.
5.
50 m
(4x + 30) m
(3x + 48)
Notes
Applying Congruence and Triangles
congruent
not congruent
Same size and shape
Different sizes or shapes
Congruence Statements – Always list the corresponding vertices in the same order.
B
Congruence statement:
E
Corresponding angles:
Corresponding sides:
A
C
F
D
Example 1
Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.
J
R
K
S
L
T
Example 2
In the diagram, DEFG  SPQR.
a. Find the value of x.
E
8 ft
D
(2x - 4) ft
Q
R
(6y + x)
102
b. Find the value of y.
84
G
68
F
12 ft
S
P
Third Angles Theorem –
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are
also congruent.
Example 3
Find m  BDC.
A
B
45
N
30
C
D
Properties of Congruent Triangles
Reflexive Property of Congruent Triangles –
Symmetric Property of Congruent Triangles –
Transitive Property of Congruent Triangles –