Download Geometry 6 - Proving Congruent Triangles

Math 20-2
Geometry: Lesson #6
Proving Congruent Triangles
Objective: By the end of this lesson, you should be able to:
- Prove, using deductive reasoning, that two triangles are congruent.
Key Point: You can prove that two triangles are congruent by using triangle congruence
theorems: SSS, SAS, ASA, and H-L.
To prove that two triangles are congruent:
1.
2.
e.g. 1) In the diagram, PS is perpendicular to QR and PQ = PR. Prove that PQS  PRS .
Statement
P
Q
Reason
R
S
e.g. 2) Given: A  D
ABC  DCB
Prove: ABC  DCB
A
D


B
C
Statement
Reason
Math 20-2
Geometry: Lesson #6
To prove that two sides or two angles of two triangles are congruent:
1.
2.
3.
e.g. 3) BC = BE and CA DE . Prove that CA = DE.
C
Statement
Reason
Statement
Reason
A
B
D
E
e.g. 4) Given: YZ = WX
XY = ZW
Prove that YZ is parallel to XW.
Z
Y
W
X
Assignment:
p. 113-115 #4-7, 9, 12, 17