One-step Proofs Geometry AC Name ____________________________ Write the theorem, definition, property or postulate that justifies the step. 1. Statement Reason _____________________ a. m 1 m 2 90 a. GIVEN b. 1 and 2 are complementary b. ___________________________________________ _____________________________________________ 2. Statement a. 1 and 2 are sup plementary Reason a. GIVEN 2 and 3 are su pplementary b. 1 and 3 are equal b. ____________________________________________ ______________________________________________ 3. Statement Reason a. 1 is a right angle a. GIVEN b. m 1 90 b. ____________________________________________ 4. Statement Reason a. 1 and 2 are complementary a. GIVEN a and b are complementary 1 a b. 2 b b. ____________________________________________ ______________________________________________ For questions #5-8, use the following diagram. C A 1 Q B D 5. Statement Reason a. 1 is a right angle a. GIVEN b. AD BC b. ___________________________________________ _____________________________________________ 6. Statement Reason a. BQ bi sects CBD a. GIVEN b. m CBQ m QBD b. ___________________________________________ _____________________________________________ 7. Statement Reason a. BQ bi sects CBD a. GIVEN b. m CBQ 1 2 m CBD b. ___________________________________________ _____________________________________________ 8. Statement Reason a. BD BC a. GIVEN b. b. ___________________________________________ CBQ and QBD arecomplementary _____________________________________________ For questions #9-15, use the following diagram. B A 1 2 D C 9. Statement Reason a. 1and 2 aresup plementary a. GIVEN b. m 1 m 2 180 b. ___________________________________________ _____________________________________________ 10. Statement a. ADB BDC Reason ADC a. ___________________________________________ 11. Statement Reason a. m 1 m 2 a. GIVEN b. AC b. ___________________________________________ DB _____________________________________________ 12. Statement a. 1 is a rightangle Reason a. GIVEN 2 is a right angle b. m 1 m 2 13. Statement a. AC DB b. 1 is a rightangle b. ___________________________________________ Reason a. GIVEN b. ___________________________________________ 14. Statement Reason a. m 1 90 a. GIVEN b. 1 is a rightangle b. ___________________________________________ 15. Statement Reason a. m 1 m 2 90 a. GIVEN m 1 m 3 b. m 3 m 2 90 b. ___________________________________________ For questions #15-18, use the following diagram. A 16. Statement a. AB + BC = AC 17. Statement B C Reason a. ___________________________________________ Reason a. AB = BC a. GIVEN b. B is the midpoint of AC b. ___________________________________________ _____________________________________________ 18. Statement Reason a. B is the midpoint of AC a. GIVEN b. AB = ½ AC b. ___________________________________________ _____________________________________________
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