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Geometry

Geometry. 4.2 Ways to Prove Triangles Congruent. Vocabulary. A. AB is opposite…. 7. C. B. AB is included between and. 7. 7. A. B. C. A is opposite…. 7. BC. 7. A is included between… and. AB. AC. W. WY is a common side of the two triangles. Z. X. Y. B.

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Geometry

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  1. Geometry 4.2 Ways to Prove Triangles Congruent

  2. Vocabulary A AB is opposite… 7 C B AB is included between and 7 7 A B C A is opposite… 7 BC 7 A is included between… and AB AC W WY is a common side of the two triangles. Z X Y

  3. B Think about this… Y A C X Z • If two triangles are congruent, then there are __ parts (angles and sides) of one triangle that are congruent to the __ corresponding parts of the other triangle. • However, it is not necessary to compare all six parts to show the triangles are congruent. • Triangles may be shown congruent by having only __ pairs of corresponding parts congruent. The next three postulates cover this. 6 6 3 angles and 3 sides. 3 angles or sides

  4. SSS Postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. S B A R C T ~ ABC = RST by SSS Post.

  5. SAS Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. F Q E P G R ~ EFG = PQR by SAS Post.

  6. ASA Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. M Y N Z L X ~ XYZ = LMN by ASA Post.

  7. ~ No Congruence. ABC = ADC by SSS Post. ~ PQS = RSQ by SAS Post. ~ EFG = EHG by ASA Post. ~ No Congruence. ABC = ZYX by SAS Post. ~ TUV = WXV by ASA Post. ~ LMN = OPQ by SSS Post.

  8. HW • P. 124-126 CE #1-10 WE #1-16 • Quiz Thursday

  9. Let’s Try This One! Given: DC bisects ACB AC = BC Prove: ADC = BDC 7 A We will use either the SSS, SAS, or the ASA Postulate. Use our proof steps on the board! D C B

  10. Let’s Try A Few Together Are the triangles congruent? If yes, write the congruence (write the three letters in correct order) and state the postulate used. If no, say no congruence. M B C 2) 1) J L ~ K ABC = CDA ~ No = N Why not? by SSS Post. D A The angle is not the included angle thus this could be the case… J A 3) ~ BAG = JOG by ASA Post. G O B

  11. Let’s try a few from the HW • Please open your books to page 125 #11 and #15

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