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

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

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

Lesson 4-4: AAS & HL Postulate B 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

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

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