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Chapter 4 Triangles

Chapter 4 Triangles. 4-3 Exploring Congruent Triangles. Triangles that are the same size and same shape are congruent triangles. Each triangle has six parts, three angles and three sides.

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Chapter 4 Triangles

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  1. Chapter 4 Triangles

  2. 4-3 Exploring Congruent Triangles • Triangles that are the same size and same shape are congruent triangles. • Each triangle has six parts, three angles and three sides. • If the corresponding six parts of one triangle are congruent to the six parts of another triangle, then the triangles are congruent. • If you slide, rotate, or flip a figure, congruence will not change. These three transformations are called congruence transformations.

  3. Definition of Congruent Triangles (CPCTC) • Two triangles are congruent if and only if their corresponding parts are congruent. • Congruence of triangles is reflexive, symmetric, and transitive.

  4. SSS AND SASCONGRUENCE POSTULATES then If 1.ABDE 4.AD 2.BCEF 5. BE ABCDEF 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

  5. SSS AND SASCONGRUENCE POSTULATES S S S Side MNQR then MNPQRS 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

  6. SSS AND SASCONGRUENCE POSTULATES The SSS Congruence Postulate is a shortcut for provingtwo triangles are congruent without using all six pairsof corresponding parts.

  7. Using the SSS Congruence Postulate Prove that PQWTSW. The marks on the diagram show that PQTS, PWTW, andQWSW. SOLUTION Paragraph Proof So by the SSS Congruence Postulate, you know that PQW TSW.

  8. SSS AND SASCONGRUENCE POSTULATES POSTULATE Side PQWX A S S then PQSWXY 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

  9. Using the SAS Congruence Postulate Prove that AEBDEC. 1 2 1 2 Statements Reasons AE  DE, BE  CE Given 1  2Vertical Angles Theorem 3 AEBDEC SAS Congruence Postulate

  10. 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 RARG. D A G R GIVEN DRAG RARG DRADRG PROVE MODELING A REAL-LIFE SITUATION Can you conclude that DRADRG? SOLUTION

  11. ASA Postulate • Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

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