Unit 5 c Proving Triangles Congruent SSS SAS

Unit 5 c Proving Triangles Congruent (SSS, SAS, ASA, AAS, HL) Lesson 4 -3: SSS, SAS, ASA 1

Postulates SSS If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. A B D C 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 2

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

Postulates ASA 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 B SAS A D C E F B D C F E 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. Lesson 4 -3: SSS, SAS, ASA 4

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. Lesson 4 -4: AAS & HL Postulate 5

Steps for Proving Triangles Congruent 1. Mark the Given. 2. Mark … Reflexive Sides / Vertical Angles 3. Choose a Method. (SSS , SAS, ASA) 4. List the Parts … in the order of the method. 5. Fill in the Reasons … why you marked the parts. 6. Is there more? Lesson 4 -3: SSS, SAS, ASA 6

Problem 1 Step 1: Mark the Given Step 2: Mark reflexive sides 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 Step 6: Is there more? A B SSS Reasons Given Reflexive Property D SSS Postulate C Lesson 4 -3: SSS, SAS, ASA 7

Problem 2 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 Step 6: Is there more? SAS Reasons Given Vertical Angles. Given SAS Postulate Lesson 4 -3: SSS, SAS, ASA 8

Problem 3 Step 1: Mark the Given Step 2: Mark reflexive sides 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 Step 6: Is there more? X W ASA Reasons Given Reflexive Postulate Y Given ASA Postulate Z Lesson 4 -3: SSS, SAS, ASA 9