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Proving Triangles
Congruent
(AAS, HL)
1
Postulates
AAS If two angles and a non included side of one triangle are
congruent to the corresponding two angles and side of a
second triangle, then the two triangles are congruent.
A
B
HL
C
E
D
A
D
F
B
C
F
E
If the hypotenuse and a leg of one right triangle are
congruent to the hypotenuse and corresponding leg of
another right triangle, then the triangles are congruent.
2
Problem 1 
Given: A  C
BE  BD
Prove: ABE  CBD
Step 1: Mark the Given
Step 2: Mark vertical angles
Step 3: Choose a Method (SSS /SAS/ASA/AAS/ HL )
Step 4: List the Parts in the order of the method
Step 5: Fill in the reasons
Statements
Reasons
Step 6: Is there more?
Given
AAS
A
C
B
E
D
1. A  C
2. ABE  CBD Vertical Angle Thm
3. BE  BD
Given
4. ABE  CBD AAS Postulate
3
Given:
Problem 2 
ABC, ADC right
AB  AD
Prove: ABC  ADC
s
Step 1: Mark the Given
Step 2: Mark reflexive sides
Step 3: Choose a Method (SSS /SAS/ASA/AAS/ HL )
Step 4: List the Parts in the order of the method
Step 5: Fill in the reasons
Statements
Reasons
Step 6: Is there more?
1.
ABC , ADC
Given
HL
A
B
C
right
s
2. AB  AD
D
3. AC  AC
Given
Reflexive Property
4. ABC  ADC HL Postulate
4