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Bell Ringer

Bell Ringer. Using Congruent Triangles. Example 1. In the diagram, AB and CD bisect each other at M . Prove that  A   B . 1. First sketch the diagram and label any congruent segments and congruent angles. 2.

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Bell Ringer

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  1. Bell Ringer

  2. Using Congruent Triangles

  3. Example 1 In the diagram, AB and CD bisect each other at M. Prove that A B. 1. First sketch the diagram and label any congruent segments and congruent angles. 2. Because Aand Bare corresponding angles in ∆ADMand ∆BCM, show that ∆ADM ∆BCMto prove that A  B. Use Corresponding Parts SOLUTION

  4. Example 1 Statements Reasons 1. AB and CD bisect each other at M. 2. MA  MB 2. Definition of segment bisector 3. AMD BMC 3. Vertical Angles Theorem 4. MD  MC 4. Definition of segment bisector 5. ∆ADM ∆BCM 5. SAS Congruence Postulate 6. A B 6. Corresponding parts of congruent triangles are congruent. Use Corresponding Parts 1. Given

  5. Example 2 Sketch the overlapping triangles separately. Mark all congruent angles and sides. Then tell what theorem or postulate you can use to show∆JGH  ∆KHG. SOLUTION 1. Sketch the triangles separately and mark any given information. Think of ∆JGHmoving to the left and ∆KHGmoving to the right. MarkGJH HKG andJHG KGH. Visualize Overlapping Triangles

  6. Example 2 2. Look at the original diagram for shared sides, shared angles, or any other information you can conclude. Add congruence marks to GHin each triangle. 3. You can use the AAS Congruence Theorem to show that∆JGH ∆KHG. Visualize Overlapping Triangles In the original diagram, GH and HG are the same side, so GHHG.

  7. Example 3 Write a proof that shows ABDE. ABC DEC CB CE AB DE 1. Sketch the triangles separately. Then label the given information and any other information you can conclude from the diagram. Use Overlapping Triangles SOLUTION In the original diagram, Cis the same in both triangles (BCA ECD).

  8. Example 3 1. Given Statements Reasons 1. ABCDEC 2. CB  CE 2. Given 3. C C 3. Reflexive Prop. of Congruence 4. ∆ABC∆DEC 4. ASA Congruence Postulate 5. AB DE 5. Corresponding parts of congruent triangles are congruent. Use Overlapping Triangles Show∆ABC∆DEC to prove thatABDE.

  9. Now You Try  1. Tell which triangle congruence theorem or postulate you would use to show that ABCD. SAS. ANSWER Use Overlapping Triangles

  10. Checkpoint Redraw the triangles separately and label all congruences. Explain how to show that the triangles or corresponding parts are congruent. 1. Given 2. GivenKJ KLandJ L,showNJML. 2. Given ANSWER Statements Reasons 1. KJKL 2. J L 3. K K 3. Reflexive Prop. of Congruence 4. ∆KJN∆KLM 4. ASA Congruence Postulate 5. NJ ML 5. Corresponding parts of triangles are . Now You Try  Use Overlapping Triangles

  11. Checkpoint 3. Given SPR QRPand Q S, show ∆PQR ∆RSP. 1. Given 2. Given ANSWER Statements Reasons 1. SPRQRP 2. Q S 3. PR  RP 3. Reflexive Prop. of Congruence 4. ∆PQR∆RSP 4. AAS Congruence Theorem Now You Try  Use Overlapping Triangles

  12. Checkpoint Now You Try 

  13. Checkpoint Now You Try 

  14. Checkpoint Now You Try 

  15. Checkpoint Now You Try 

  16. Page 268

  17. Complete Pages 268-270 #s 6-20 Even Only

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