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Proving Overlapping Triangles

Proving Overlapping Triangles. Math 2 - Lesson 23 Mr. Lopez. Overlapping Triangles. Overlapping Triangles: Some triangle relations are difficult to see because the triangles overlap. To make things easier separate and redraw the triangles. C. A. D. B. E. F. C. A. D. B. E. F. E.

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Proving Overlapping Triangles

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  1. Proving Overlapping Triangles Math 2 - Lesson 23 Mr. Lopez

  2. Overlapping Triangles • Overlapping Triangles: • Some triangle relations are difficult to see because the triangles overlap. • To make things easier separate and redraw the triangles. C A D B E F C A D B E F E F

  3. C A B D E F Proofs with Overlapping Triangles Given: 1 =  2, AB  BF, CD  DE, BE = FD Prove: ΔAFB = ΔCED Since the two triangles you want to prove overlap, redraw and separate them. G 1 2

  4. Proofs with Overlapping Triangles • Now that they are separated, mark the diagrams by what’s given to help you visualize what you have and what you need C A 1 2 D B E F E F C A 2 1 D E F E F B

  5. Proofs with Overlapping Triangles C • Now that they are separated you can see what you have and what you need a little clearer. • What You Have: Rt ’s, 1 = 2 and part of a line segment • What You Need: The completion of the line segment to prove the triangles are congruent using ASA. A 1 2 D E F E F B

  6. Proofs with Overlapping Triangles 1. Given ------- 2.Defintion of  lines ------- 3. Def of right angles 4. Substitution 5. Reflexive 6. Partition Post 7. Addition 8. Substitution 9. ASA 1. 1 =  2, AB  BF, CD  DE, BE = DF 2. B and D are right ’s. 3. B = 90, D = 90 4.  B = D 5. EF = EF 6. BF = BE + EF ED = DF + EF 7. BE + EF = DF + EF 8. BF = ED 9. ΔAFB = ΔCED

  7. You Try! Given: AD = AE B = C Part a: Prove: ΔADC = ΔAEB Part B: Continue the proof and prove DC = EB A E D B C

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