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Lesson 4-3

Proving Triangles Congruent. Lesson 4-3. (SSS, SAS, ASA, AAS, HL). A. D. F. B. C. E. Postulates. If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. SSS. Included Angle:.

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Lesson 4-3

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

  2. A D F B C E Postulates If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. SSS 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 Angle: * * * Included Side: Lesson 4-3: SSS, SAS, ASA

  4. A A D D B C B C F F E E 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 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. A B C D Problem 1  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 Step 6: Is there more? Given Given Reflexive Property SSS Postulate Lesson 4-3: SSS, SAS, ASA

  7. Problem 2  Step 1: Mark the Given Step 2: Mark vertical angles 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 Step 6: Is there more? Given Vertical Angles. Given SAS Postulate Lesson 4-3: SSS, SAS, ASA

  8. 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 Step 6: Is there more? Given Reflexive Postulate Given ASA Postulate Lesson 4-3: SSS, SAS, ASA

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

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

  11. 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 Step 6: Is there more? Given Vertical Angle Thm Given AAS Postulate Lesson 4-4: AAS & HL Postulate

  12. 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 Step 6: Is there more? Given Given Reflexive Property HL Postulate Lesson 4-4: AAS & HL Postulate

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