Download Lesson 4.5 Are There Other Congruence Shortcuts? notes

4.5 Are There Other Congruence Shortcuts?
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If two angles and the included side in one triangle are congruent to two angles and the included side
of another triangle, then the two triangles are congruent.
E
B
A
if A  ____
AB  ____
F
D
C
B _____
ABC  ______
then
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If two angles and the non-included side of one triangle are congruent to two angles and the nonincluded side of another triangle, then the two triangles are congruent.
E
B
A
if A  ____
C
B  _____
F
D
BC  ____,
then
Geometry Lesson 4.5: Are There Other Congruence Shortcuts?
ABC  ______
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If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another
right triangle, then the two triangles are congruent.
A
D
C
B
F
E
If C is a right angle, ______ is a right angle, AB  ______, BC  _____,
then
ABC  _______
** Note: In order to use HL, you must first establish that you have right triangles**
**Remember: SSA is not a valid Congruency Shortcut and AAA is not a valid
Congruency Shortcut. **
Geometry Lesson 4.5: Are There Other Congruence Shortcuts?
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Example 1: Which pairs of triangles are congruent? Write the correct congruency statement and tell
which postulate or theorem allows you to determine the triangles’ congruency.
E
H
B
A
G
D
F
C
K
J
I
Example 2: Which pairs of triangles are congruent? Write the correct congruency statement and tell
which postulate or theorem allows you to determine the triangles’ congruency.
W
S
Q
L
X
R
M
NP
O
T
Y
V
Z
U
Geometry Lesson 4.5: Are There Other Congruence Shortcuts?
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Example 3: Which pairs of triangles are congruent? Write the correct congruency statement and tell
which postulate or theorem allows you to determine the triangles’ congruency.
ADB 
______
D
A
STU 
C
______
W
S
U
V
T
B
M
O
E
L
MOE 
_______
Homework: pp. 227 – 228 => 1 – 16
Geometry Lesson 4.5: Are There Other Congruence Shortcuts?
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