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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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**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 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**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**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**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**B**3 Reflexive AC AC D E DCA EAC SSS SSS DCA EAC CPCTC A C Prove: DCA EAC**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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