Download 4.3-4.4 Proving Triangles Congruent Using SSS, SAS, ASA, AAS

4.3­4.4 Proving Triangles Congruent Using SSS, SAS, ASA, AAS (work).notebook
November 09, 2015
4.3 ‐ 4.4 PROVING TRIANGLES CONGRUENT
Postulate 19: SSS Postulate
If the sides of one triangle are congruent to the
sides of a second triangle, then the triangles are
congruent.
C
X
M
H
A
Z
Example 1
Given STU with vertices S(0, 5), T(0, 0), and
U(‐2, 0) and XYZ with vertices X(4, 8),
Y(4, 3), and Z(6, 3), determine if
~ XYZ.
STU =
4.3­4.4 Proving Triangles Congruent Using SSS, SAS, ASA, AAS (work).notebook
November 09, 2015
Postulate 20: SAS Postulate
If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the
triangles are congruent.
B
The included angle
is the angle formed
by two given sides.
W
J
U
K
G
Example 2
Write a proof for the following.
Given: X is the midpoint of BD.
X is the midpoint of AC.
~ BXA
Prove:
DXC =
Statements
A
D
X
C
Reasons
B
4.3­4.4 Proving Triangles Congruent Using SSS, SAS, ASA, AAS (work).notebook
November 09, 2015
Postulate 21: ASA Postulate
If two angles and the included side of one
triangle are congruent to two angles and the
included side of another triangle, the triangles
L
are congruent.
The included side
is the side of the triangle
formed between
two given angles.
R
Y
S
Q
D
V
Example 3
Write a proof for the following.
~ US
Given: VR RS, UT SU, RS =
~ TUS
Prove:
VRS =
Statements
Reasons
R
S
U
T
4.3­4.4 Proving Triangles Congruent Using SSS, SAS, ASA, AAS (work).notebook
November 09, 2015
Theorem 4‐6: AAS Theorem
If two angles and a nonincluded side of a
triangle are congruent to the corresponding
two angles and a side of a second triangle, the
two triangles are congruent.
V
C
T
N
O
A
Example 4
Write a two‐column proof.
Given:
PSU ~
= PTR
SU ~
= TR
~ TRP
Prove: SUP =
T
S
R
U
P
Statements
Reasons
4.3­4.4 Proving Triangles Congruent Using SSS, SAS, ASA, AAS (work).notebook
November 09, 2015
Example 5
Write a two‐column proof.
Given:
1 and 2 are right angles.
S
ST ~
= TP
5
~ PTR
Prove: STR =
1
T
3
4
2
R
6
P
Statements
Reasons
Example 6
Write a two‐column proof.
A
Given: BE bisects AD.
~ D
A=
~ DEC
Prove: ABE =
B
Statements
Reasons
C
1
E
2
D
4.3­4.4 Proving Triangles Congruent Using SSS, SAS, ASA, AAS (work).notebook
November 09, 2015
Theorem 4‐8: HL Theorem
If the hypotenuse and a leg of a right triangle
are congruent to the hypotenuse and a leg of a
second right triangle, then the two triangles
are congruent.
F
B
M
Z
H
Example 7
Write a two‐column proof.
Given: AE CD
AC ~
=AD
Prove: ACE ~
= ADE
Statements
A
A
C
Reasons
1 2
E
D