1. CCGPS Analytic Geometry
Proving Triangles Congruent
(SSS, SAS, ASA, AAS, HL)
Unit 1

2. SSS
If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. A B C D E F
Unit 1 : SSS, SAS, ASA

3. Side-Side-Side SSS
If all 3 sides of 2 triangles are congruent, the triangles are congruent.
If AB  ED,
and AC  EF
BC  DF,
, then the 2 triangles are congruent 
Make sure that you write the congruency statement so that the corresponding
vertices (and thus the corresponding sides) are in the same position in the
congruency statement.
∆ABC  ∆EDF
not ∆ABC  ∆DEF

4. * * * Included Angles Included Angle: Included Angle
In a triangle, the angle formed by two sides is the included angle for the two sides.
Lesson 4-3: SSS, SAS, ASA

5. * * * Included Sides Included Side: Included Side:
The side of a triangle that forms a side of two given angles.
Included Side: * * *
Lesson 4-3: SSS, SAS, ASA 5

6. ASA Angle Side Angle
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. A A B C D E F S
Sides AB = ED A 6
Lesson 4-3: SSS, SAS, ASA

7. SAS Side Angle Side
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. S A S
Lesson 4-3: SSS, SAS, ASA 7

8. 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

9. Problem 1 - SSS AB @ CD BC DA AC CA 1. 2. 3. A B D C Statements
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? 1. AB @ CD 2. BC DA 3. AC CA
Given A B D C
Given
Reflexive Property
SSS Postulate
Lesson 4-3: SSS, SAS, ASA

10. Unit 1 CCGPS Analytic Geom. SSS, SAS, ASA
Problem 2
Step 1: Mark the Given
Step 2: Mark vertical angles congruent
SAS
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
Unit 1 CCGPS Analytic Geom. SSS, SAS, ASA

11. Problem 3 ASA X W Y Z Statements Reasons 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

12. AAS Angle Angle Side (corresponding)
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.
IS NOT CONGRUENT WITH EITHER OF THE OTHER 2
Congruent Angles and side DO NOT correspond..

13. Hypotenuse Leg 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

14. Problem 1  AAS Statements Reasons 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

15. Problem 2  HL Statements Reasons 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