Download Lesson 4.4-4.6 - Triangle Congruence.notebook

Lesson 4.4­4.6 ­ Triangle Congruence.notebook
October 03, 2016
Lesson 4.4 - 4.6
Triangle Congruence
Objective: To prove two triangles congruent
using SSS, SAS HL, ASA, and AAS.
Defintions:
Included Angle: Angle formed by two sides
side
included angle
side
Included Side: Side between two angles
angle
angle
Included side
K
L
N
M
Name the required angle or side:
1) The included angle for KN and KM
2) The side opposite
KML
3) The angle opposite KN
4) The included side for LKM and KML
1
Lesson 4.4­4.6 ­ Triangle Congruence.notebook
October 03, 2016
It isn't necessary to show all 6 parts are
congruent to prove 2 triangles are congruent.
There are 5 "shortcuts" that can be used:
4 Postulates:
1) SSS
2) SAS
3) ASA
4) AAS
1 Theorem:
5) HL
*only used for right triangle
1) SSS Congruence Postulate: Side-Side-Side
• If 3 sides of one triangle are congruent to 3 sides
of another triangle, then the two triangles are
congruent.
A
B
C
AB ≅ MN
If BC ≅ NP
AC ≅ MP
then ΔABC ≅ Δ MNP
2) SAS Congruence Postulate: Side-Angle-Side
• If 2 sides and an included angle of one triangle are
congruent to 2 sides and an included angle of a second
triangle, then the two triangles are congruent.
Q
B
A
C
then, ΔPQS ≅ΔABC
2
Lesson 4.4­4.6 ­ Triangle Congruence.notebook
October 03, 2016
3) ASA Congruence Postulate: Angle-Side-Angle
• If two angles and an included side of one triangle are
congruent to two angles and an included side of another
triangle, then the two triangles are congruent.
then, Δ ABC ≅ Δ DEF
4) AAS Congruence Postulate: Angle-Angle-Side
• If two angles and a non-included side of one triangle are
congruent to two angles and a non-included side of a second
triangle, then the two triangles are congruent.
then, Δ ABC ≅ Δ DEF
Right Triangles
Hypotenuse = longest side, across from the right angle
Legs = other two sides, touch the right angle
3
Lesson 4.4­4.6 ­ Triangle Congruence.notebook
October 03, 2016
5) HL Congruence Theorem : Hypotenuse-Leg
• If the hypotenuse and a leg of a right triangle are
congruent to the hypotenuse and leg of a second right
triangle, then the two triangles are congruent.
If ΔABC and ΔDEF are right triangles,
A
D
H AC ≅ DF
L BC ≅ EF
then, Δ ABC ≅ Δ DEF
B
C
E
F
Which postulate, if any, can be used to prove the triangles are congruent. Write the congruence statement if possible.
1) A
E
W
F
N
D
2)
P
3)
K
U
N
4
Lesson 4.4­4.6 ­ Triangle Congruence.notebook
October 03, 2016
Given: CD EA, AD is perpendicular bisector of CE
C
Prove: ΔABE ΔDBC
Statements
A
Reasons
B
D
E
Given: WJ KZ, <W and <K are right angles
Prove: ΔWJZ ΔKZJ
Statements
W
Z
J
K
Reasons
5