Proving Triangles Congruent Lesson 4-3 Proving Triangles Congruent (SSS, SAS, ASA) Lesson 4-3: SSS, SAS, ASA

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

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

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

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

Problem 1  SSS AB @ CD BC DA AC CA 1. 2. 3. 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? 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

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

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