1. Proving Triangles Congruent
Lesson 4-3
Proving Triangles Congruent
(SSS, SAS, ASA, AAS, HL)
Lesson 4-3: SSS, SAS, ASA

2. Postulates
If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
SSS A B C D E F
Included Angle:
In a triangle, the angle formed by two sides is the included angle for the two sides.
Included Side:
The side of a triangle that forms a side of two given angles.
Lesson 4-3: SSS, SAS, ASA

3. Included Angles & Sides* * *
Included Side:
Lesson 4-3: SSS, SAS, ASA

4. Postulates
If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the triangles are congruent.
ASA A B C D E F A B C D E F
If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent.
SAS
Lesson 4-3: SSS, SAS, ASA

5. Steps for Proving Triangles Congruent
Mark the Given.
Mark … Reflexive Sides / Vertical Angles
Choose a Method. (SSS , SAS, ASA)
List the Parts … in the order of the method.
Fill in the Reasons … why you marked the parts.
Is there more?
Lesson 4-3: SSS, SAS, ASA

6. Problem 1  SSS A B D C Step 1: Mark the Given
Step 2: Mark reflexive sides
SSS
Step 3: Choose a Method (SSS /SAS/ASA )
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 A B D C
Given
Reflexive Property
SSS Postulate
Lesson 4-3: SSS, SAS, ASA

7. Problem 2  SAS Step 1: Mark the Given Step 2: Mark vertical angles
Step 3: Choose a Method (SSS /SAS/ASA)
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
Vertical Angles.
Given
SAS Postulate
Lesson 4-3: SSS, SAS, ASA

8. ASA X W Y Z Problem 3 Step 1: Mark the Given
Step 2: Mark reflexive sides
ASA
Step 3: Choose a Method (SSS /SAS/ASA)
Step 4: List the Parts in the order of the method
Step 5: Fill in the reasons
Statements
Reasons
Step 6: Is there more? Z W Y X
Given
Reflexive Postulate
Given
ASA Postulate
Lesson 4-3: SSS, SAS, ASA

9. Lesson 4-4: AAS & HL Postulate
Theorem
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.
AAS A B C D E F
Lesson 4-4: AAS & HL Postulate

10. Lesson 4-4: AAS & HL PostulateB C D E F 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.
Lesson 4-4: AAS & HL Postulate

11. Lesson 4-4: AAS & HL Postulate
Problem 1 
Step 1: Mark the Given
Step 2: Mark vertical angles
AAS
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
Vertical Angle Thm
Given
AAS Postulate
Lesson 4-4: AAS & HL Postulate

12. Lesson 4-4: AAS & HL Postulate
Problem 2 
Step 1: Mark the Given
Step 2: Mark reflexive sides HL
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
Given
Reflexive Property
HL Postulate
Lesson 4-4: AAS & HL Postulate