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Warm Up

Prove Triangles Congruent by SAS and HL. Warm Up. Lesson Presentation. Lesson Quiz. Given: DF bisects CE , DC DE. Prove: ∆CDF ∆EDF. C. F. D. E. ANSWER.

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Warm Up

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  1. Prove Triangles Congruent by SAS and HL Warm Up Lesson Presentation Lesson Quiz

  2. Given: DF bisects CE, DC DE Prove: ∆CDF ∆EDF C F D E ANSWER It is given thatDC DEand DFbisects CE.CF EF by the def. of bisector.DF DF by the Refl. Prop. of Segs. So ∆CDF∆EDFby the SSS Post. Warm-Up

  3. BC DA,BC AD ABCCDA ABCCDA STATEMENTS REASONS Given S BC DA Given BC AD BCADAC A Alternate Interior Angles Theorem S ACCA Reflexive Property of Congruence 5. SAS Congruence Postulate 5. Example 1 Write a proof. GIVEN: PROVE:

  4. Because they are vertical angles, PMQRMS. All points on a circle are the same distance from the center, so MP, MQ, MR, and MSare all equal. ANSWER MRSand MPQ are congruent by the SAS Congruence Postulate. Example 2 In the diagram, QSand RPpass through the center Mof the circle. What can you conclude about MRSand MPQ? SOLUTION

  5. Prove that SVRUVR ANSWER Guided Practice In the diagram, ABCDis a square with four congruent sides and four right angles. R, S, T, and Uare the midpoints of the sides of ABCD. Also, RT SUand . SU VU

  6. BSRDUT Prove that ANSWER Guided Practice In the diagram, ABCDis a square with four congruent sides and four right angles. R, S, T, and Uare the midpoints of the sides of ABCD. Also, RT SUand . SU VU

  7. Guided Practice

  8. WY XZ,WZ ZY, XY ZY GIVEN: WYZXZY PROVE: Redraw the triangles so they are side by side with corresponding parts in the same position. Mark the given information in the diagram. Example 3 Write a proof. SOLUTION

  9. STATEMENTS REASONS Given WY XZ H Given WZ ZY, XY ZY Definition of lines Z andY are right angles Definition of a right triangle WYZand XZY are right triangles. ZY YZ L Reflexive Property of Congruence WYZXZY HL Congruence Theorem Example 3

  10. You are making a canvas sign to hang on the triangular wall over the door to the barn shown in the picture. You think you can use two identical triangular sheets of canvas. You knowthatRP QS and PQ PS. What postulate or theorem can you use to conclude that PQRPSR? Sign Making Example 4

  11. You are given that PQ PS. By the Reflexive Property, RP RP. By the definition of perpendicular lines, both RPQ and RPSare right angles, so they are congruent. So, two sides and their included angle are congruent. ANSWER You can use the SAS Congruence Postulate to conclude that . PQRPSR Example 4 SOLUTION

  12. Redraw ACBand DBCside by side with corresponding parts in the same position. ANSWER Guided Practice Use the diagram at the right.

  13. Use the information in the diagram to prove that ACBDBC ANSWER Guided Practice Use the diagram at the right.

  14. 1. ABE,CBD ANSWER SAS Post. Lesson Quiz Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.

  15. 2. FGH,HJK ANSWER HL Thm. Lesson Quiz Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.

  16. State a third congruence that would allow you to prove RSTXYZ by the SAS Congruence postulate. 3. ST YZ, RS XY ANSWER SY. Lesson Quiz

  17. State a third congruence that would allow you to prove RSTXYZ by the SAS Congruence postulate. 4. T Z, RT XZ ANSWER STYZ . Lesson Quiz

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