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Unit 1 1 CCGPS Analytic Geometry Proving Triangles Congruent (SSS, SAS, ASA, AAS, HL)

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Unit 1 : SSS, SAS, ASA 2 SSS If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. A B C D E F

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Side-Side-Side SSS If all 3 sides of 2 triangles are congruent, the triangles are congruent. If AB ED, Make sure that you write the congruency statement so that the corresponding vertices (and thus the corresponding sides) are in the same position in the congruency statement. ∆ABC ∆EDF BC DF, and AC EF, then the 2 triangles are congruent not ∆ABC ∆DEF

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Lesson 4-3: SSS, SAS, ASA 4 Included Angles Included Angle: * ** In a triangle, the angle formed by two sides is the included angle for the two sides. Included Angle

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Lesson 4-3: SSS, SAS, ASA 5 Included Sides Included Side: * ** The side of a triangle that forms a side of two given angles.

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Lesson 4-3: SSS, SAS, ASA 6 ASA Angle Side Angle 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 BC D E F Sides AB = ED A S A

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Lesson 4-3: SSS, SAS, ASA7 SAS Side Angle Side 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. S S A

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Lesson 4-3: SSS, SAS, ASA 8 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?

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Lesson 4-3: SSS, SAS, ASA 9 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 1. AB CD 2. BC DA 3. AC CA

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Unit 1 CCGPS Analytic Geom. SSS, SAS, ASA 10 Problem 2 Step 1: Mark the Given Step 2: Mark vertical angles congruent 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

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Lesson 4-3: SSS, SAS, ASA 11 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

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AAS Angle Angle Side (corresponding) 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. IS NOT CONGRUENT WITH EITHER OF THE OTHER 2 Congruent Angles and side DO NOT correspond..

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Hypotenuse Leg 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

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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

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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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