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SSS AND SAS C ONGRUENCE P OSTULATES. then. If. 1. AB DE. 4. A D. 2. BC EF. 5. B E. ABC DEF. 3. AC DF. 6. C F. If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Sides are congruent. Angles are congruent.
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SSS AND SASCONGRUENCE POSTULATES then If 1.ABDE 4.AD 2.BCEF 5. BE ABCDEF 3.ACDF 6.CF If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Sides are congruent Angles are congruent Triangles are congruent and
SSS AND SASCONGRUENCE POSTULATES S S S Side MNQR then MNPQRS Side NPRS Side PMSQ POSTULATE POSTULATE 19Side -Side -Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sidesof a second triangle, then the two triangles are congruent. If
SSS AND SASCONGRUENCE POSTULATES The SSS Congruence Postulate is a shortcut for provingtwo triangles are congruent without using all six pairsof corresponding parts.
Using the SSS Congruence Postulate Prove that PQWTSW. The marks on the diagram show that PQTS, PWTW, andQWSW. SOLUTION Paragraph Proof So by the SSS Congruence Postulate, you know that PQW TSW.
SSS AND SASCONGRUENCE POSTULATES POSTULATE Side PQWX A S S then PQSWXY Angle QX Side QSXY POSTULATE 20Side-Angle-Side (SAS) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If
Using the SAS Congruence Postulate Prove that AEBDEC. 1 2 1 2 Statements Reasons AE DE, BE CE Given 1 2Vertical Angles Theorem 3 AEBDEC SAS Congruence Postulate
Proving Triangles Congruent ARCHITECTURE You are designing the window shown in the drawing. You want to make DRAcongruent to DRG. You design the window so that DRAG and RARG. D A G R GIVEN DRAG RARG DRADRG PROVE MODELING A REAL-LIFE SITUATION Can you conclude that DRADRG? SOLUTION
Proving Triangles Congruent GIVEN RARG DRADRG PROVE 1 2 6 3 4 5 Statements Reasons Given DRAG If 2 lines are , then they form 4 right angles. DRA and DRG are right angles. Right Angle Congruence Theorem DRADRG DRAG Given RARG DRDR Reflexive Property of Congruence SAS Congruence Postulate DRADRG D A R G
Congruent Triangles in a Coordinate Plane AC FH ABFG Use the SSS Congruence Postulate to show that ABCFGH. SOLUTION AC = 3 and FH= 3 AB = 5 and FG= 5
Congruent Triangles in a Coordinate Plane d = (x2 – x1 )2+ (y2 – y1 )2 d = (x2 – x1 )2+ (y2 – y1 )2 BC = (–4 – (–7))2+ (5– 0)2 GH = (6 – 1)2+ (5– 2)2 = 32+ 52 = 52+ 32 = 34 = 34 Use the distance formula to find lengths BC and GH.
Congruent Triangles in a Coordinate Plane BCGH BC = 34 and GH= 34 All three pairs of corresponding sides are congruent, ABCFGH by the SSS Congruence Postulate.