Download Identifying Congruent Figures

Opener
Sect. 4.2 Congruence and
Triangles
Goal 1
Identifying Congruent Figures
Goal 2
Proving Triangles are
Congruent
Identifying Congruent Figures
Two geometric figures are congruent if
they are the same size and shape
• Their
corresponding angles and sides are equal.
Example:
The pentagons
are congruent.
Identifying Congruent Figures
Congruent Triangles
Figures that have the same size and shape
Example:
The triangles are congruent.
Identifying Congruent Figures
If two figures are congruent, then their corresponding
parts are congruent. Look at the corresponding parts of
ABC and DFE. A
B
ABC 
C
D
DFE
F
E
A triangle has three sides and three angles. If two triangles are congruent,
then the sides and angles that match are called corresponding parts.
A corresponds to D
B corresponds to F
C corresponds to E
side AB corresponds to side DF
side BC corresponds to side FE
side CA corresponds to side ED.
Identifying Congruent Figures
Write a congruence
statement for the two
triangles. Then identify all
pairs of congruent
A
corresponding parts.
B
E
98°
98°
C
D
F
Identify all the pairs of congruent parts if DWV  PJS
Regardless of how the diagram appears you can
determine all the congruent corresponding parts based
on the congruence statement provided.
V
D
P
W
J
S
Identifying Congruent Figures
Corresponding Parts of Congruent
Triangles are Congruent
CPCTC
Identifying Congruent Figures
In the diagram, ABCD  KJHL
1) Find the value of x
2) Find the value of y
J
A
9 cm
B
91°
(5y - 12)°
H
(4x - 3) cm
D
86°
113°
6 cm
C
K
L
Identifying Congruent Figures
Theorem 4.3 Third Angles Theorem
If two angles of one triangle are congruent to two
angles of a second triangle, then the third angles of
the triangles are congruent.
If A  D and B  F,
Then C  E
Identifying Congruent Figures
Find the value of x.
B
87°
A
22°
C
F
(4X + 15)°
E
D
Proving Triangles are Congruent
Given: MN  QP; MN || PQ;
M
N
O is midpoint of MQ and PN
Prove: MNO  QPO
1. MN  QP
1. Given
2. MN || QP
2. Given
3. OMN  OQP
3. Alt Interior Angles
4. ONM  OPQ
4. Alt Interior Angles
5. MON  POQ
5. Vertical Angles
6. O is the midpoint of
MQ and PN
6. Given
7. MO  OQ, PO  ON
7. Def of a midpoint
8. ∆MNO  ∆QPO
8. CPCTC
O
P
Q
Homework
4.2 Exs. 10 – 28 even, 46-56 even