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# Overlapping Triangle Proofs

Overlapping Triangle Proofs. A. 2. If 2 sides of a triangle are congruent then the angles opposite the sides are congruent. ABC  ACB. D. E. BC  BC. Reflexive. BDC  CEB. SAS  SAS. B. C. BE  CD. CPCTC. Prove: BE  CD. D. C. ADC is right.

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## Overlapping Triangle Proofs

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1. Overlapping Triangle Proofs

2. A 2. If 2 sides of a triangle are congruent then the angles opposite the sides are congruent. ABC  ACB D E BC  BC Reflexive BDC  CEB SAS  SAS B C BE  CD CPCTC Prove: BE  CD

3. D C ADC is right Perpendicular lines form right angles BCD is right ADC  BCD All Right angles are congruent A B CD  CD Reflexive Prove: AC = BD SAS  SAS ADC  BCD CPCTC AC  BD

4. D If 2 lines are parallel, then alternate interior angles are congruent A  C C DFC supplement to 1 BEA supplement to 2 Linear pairs are supplementary. E 2 If 2 angles are congruent then their supplements are congruent DFC  BEA 1 F FE  FE Reflexive A AF + FE  CE + FE AE CF Addition B ABE  DCF ASA  ASA Prove: ABE  DCF

5. Homework Problems R S P N P is right N is right Perpendicular lines form right angles. All Right angles are congruent P  N RS  RS Reflexive L M PR + RS = NS + RS PS = NR Addition SAS  SAS LPS  MNR Prove: LPS  MNR

6. B 1  ½ BCA 2  ½ BAC A bisector divides an angle into 2 congruent angles. D E 1  2 Division 2 1 AC  AC Reflexive A C ADC  CEA ASA  ASA Prove: ADC  CEA

7. B 3 Reflexive AC  AC D E DCA  EAC SSS  SSS DCA  EAC CPCTC A C Prove: DCA  EAC

8. C 4. 1 2 Reflexive DE  DE AE - DE  BD - DE AD  BE Subtraction D B A E ACD  BCE SSS  SSS Prove: 1  2 1  2 CPCTC

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