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**Proving Triangles Congruent**

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

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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

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**Included Angles & Sides**

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

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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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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