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Geometry Congruence Proofs and Triangle Congruence Theorems Overview

This document provides an overview of essential geometry concepts related to triangle congruence and angle relationships. Key theorems discussed include ASA, SAS, and SSS for proving triangle congruence. It also covers properties of angles, including alternate interior angles and vertical angles, establishing their congruences. Additionally, definitions of bisectors and perpendicularity are explored. The text appears to reference test review materials, practicing geometric proofs, and applying laws related to transitivity and detachment.

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Geometry Congruence Proofs and Triangle Congruence Theorems Overview

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  1. BAS, ASA • EWX, SAS • Not Congruent • BCA, SSS • Given, Alternate Interior angles are congruent, Vertical angles are congruent, ASA • BA is the perpendicular Bisector of MN / Given  MA NA / definition of bisector  mMAB =90°, mNAB =90° / def. of perp. • MAB NAB / all right angles are congruent AB AB / Reflexive Property  BAM  BAN / SAS Unit 2 Test Review Answers 13.5 60°, 6, 12 2 540 in2 48 No JHG, SAS KIN, AA Not Similar LHR, SSS 45, Corresponding angles, b, e MNO, HL ORF, AAS

  2. x = 35°, y = 24 • x = 40°, y = 6 • x = 6, y = 12 Trapezoid Parallelogram See Chart  20° 65° CorrespondingParts of CongruentTriangles are Congruent C A C x = 7, y =5 x = 13, y = 1, z = 19 12 If the students talk, they will not be able to learn. / Law of Transitivity Jacob will make good grades. / Law of Detachment It is not raining Law of Contra positives Converse: If two angles are congruent, then they are vertical. Inverse: If two angles are not vertical, then they are not congruent. Contrapostive: If two angles are not congruent, then they are not vertical.

  3. BAS, ASA • EWX, SAS • Not Congruent • BCA, SSS • Given, Alternate Interior angles are congruent, Vertical angles are congruent, ASA • BA is the perpendicular Bisector of MN / Given  MA NA / definition of bisector  mMAB =90°, mNAB =90° / def. of perp. • MAB NAB / all right angles are congruent AB AB / Reflexive Property  BAM  BAN / SAS Unit 2 Test Review Answers 13.5 60°, 6, 12 2 540 in2 48 No JHG, SAS KIN, AA Not Similar LHR, SSS 45, Corresponding angles, b, e MNO, HL ORF, AAS

  4. x = 35°, y = 24 • x = 40°, y = 6 • x = 6, y = 12 Trapezoid Parallelogram See Chart  20° 65° CorrespondingParts of CongruentTriangles are Congruent C A C x = 7, y =5 x = 13, y = 1, z = 19 12 If the students talk, they will not be able to learn. / Law of Transitivity Jacob will make good grades. / Law of Detachment It is not raining Law of Contra positives Converse: If two angles are congruent, then they are vertical. Inverse: If two angles are not vertical, then they are not congruent. Contrapostive: If two angles are not congruent, then they are not vertical.

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