Lesson 4-4: AAS & HL Postulate 1

Lesson 4-4

Proving Triangles Congruent

(AAS, HL)

Lesson 4-4: AAS & HL Postulate 2

PostulatesAAS 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.

HL 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.

A

B C

D

E F

A

B C

D

E F

Lesson 4-4: AAS & HL Postulate 3

Problem 1

Statements Reasons

Step 1: Mark the Given Step 2: Mark vertical anglesStep 3: Choose a Method (SSS /SAS/ASA/AAS/ HL )Step 4: List the Parts in the order of the methodStep 5: Fill in the reasonsStep 6: Is there more?

AAS

Given

Given

Vertical Angle Thm

AAS Postulate

Given: A C BE BDProve: ABE CBD

E

C

D

AB

1. A C2. ABE CBD

3. BE BD

4. ABE CBD

Lesson 4-4: AAS & HL Postulate 4

Problem 2

3. AC AC2. AB AD

1. ,ABC ADCright s

Step 1: Mark the Given Step 2: Mark reflexive sidesStep 3: Choose a Method (SSS /SAS/ASA/AAS/ HL )Step 4: List the Parts in the order of the methodStep 5: Fill in the reasonsStep 6: Is there more?

HL

Given

Given

Reflexive Property

HL Postulate

Given: ABC, ADC right s AB ADProve: ABC ADC

CB D

A

4. ABC ADC

Statements Reasons