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

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Presentation on theme: "Lesson 4-3: SSS, SAS, ASA 1 Lesson 4-3 Proving Triangles Congruent (SSS, SAS, ASA, AAS, HL)"— Presentation transcript:

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

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

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

4 Lesson 4-3: SSS, SAS, ASA 4 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. SAS 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. A BC D E F A BC D E F

5 Lesson 4-3: SSS, SAS, ASA 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?

6 Lesson 4-3: SSS, SAS, ASA 6 Problem 1  StatementsReasons 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 Step 6: Is there more? AB D C SSS Given Reflexive Property SSS Postulate

7 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 Step 6: Is there more? SAS Given Vertical Angles. SAS Postulate StatementsReasons

8 Lesson 4-3: SSS, SAS, ASA 8 Problem 3 StatementsReasons 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 Step 6: Is there more? ASA Given Reflexive Postulate ASA Postulate Z W Y X

9 Lesson 4-4: AAS & HL Postulate 9 Theorem 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 BC D E F

10 Lesson 4-4: AAS & HL Postulate 10 Postulate 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 BC D E F

11 Lesson 4-4: AAS & HL Postulate 11 Problem 1  StatementsReasons Step 1: Mark the Given Step 2: Mark vertical angles 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? AAS Given Vertical Angle Thm AAS Postulate

12 Lesson 4-4: AAS & HL Postulate 12 Problem 2  Step 1: Mark the Given Step 2: Mark reflexive sides 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? HL Given Reflexive Property HL Postulate StatementsReasons


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