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Given: ABCD is a parallelogram, AC BD. Prove: ABCD is a rectangle. Statement Reason 1. ABCD is a parallelogram, ACBD. 2. AD BC 3. CD CD 4. AADC ABCD 5. LADC LBCD 6. LADC LABC LBCD LDAB 7. LABC LDAB 8. MLABC + M2DAB 9. 2MLABC = 180° Given 1. 2. 3. 4. 5. Substitution = 180° 6. 7. = 90° 11. ZABC is right angle 12. MLABC = M

Given: ABCD is a parallelogram, AC BD. Prove: ABCD is a rectangle. Statement Reason 1. ABCD is a parallelogram, ACBD. 2. AD BC 3. CD CD 4. AADC ABCD 5. LADC LBCD 6. LADC LABC LBCD LDAB 7. LABC LDAB 8. MLABC + M2DAB 9. 2MLABC = 180° Given 1. 2. 3. 4. 5. Substitution = 180° 6. 7. = 90° 11. ZABC is right angle 12. MLABC = M

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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B Given: ABCD is a parallelogram, AC = BD. Prove: ABCD is a rectangle. D Statement Reason 1. ABCD is a parallelogram, AC BD. Given 2. AD = BC 3. CD = CD 4. AADC = ABCD 5. LADC = LBCD 6. LADC LABC ZBCD LDAB 7. LABC LDAB 8. MLABC + MLDAB = 9. 2MLABC 1. 2. 3. 4. 5. Substitution 180° 6. 180° 7. %3D 10. MLABC = 90° 8. 11. ZABC is right angle Multiplication Property of Equality 12. MLABC = M<DAB = MLADC = MLBCD 9. 13. ABCD is a rectangle 10. Choose your answer below. Write the LETTER of your answer on the REASON Column. A. Consecutive angles of a parallelogram are supplementary B. Opposite sides of a parallelogram are congruent C. Opposite angles of a parallelogram are congruent D. Substitution and closure E. Reflexive F. Corresponding Parts of Congruent Triangles are Congruent (CPCTC) G. Side-Side-Side Triangle Congruence (SSS) H. Definition of rectangle I. Definition of right angles J. Transitive
Transcribed Image Text:B Given: ABCD is a parallelogram, AC = BD. Prove: ABCD is a rectangle. D Statement Reason 1. ABCD is a parallelogram, AC BD. Given 2. AD = BC 3. CD = CD 4. AADC = ABCD 5. LADC = LBCD 6. LADC LABC ZBCD LDAB 7. LABC LDAB 8. MLABC + MLDAB = 9. 2MLABC 1. 2. 3. 4. 5. Substitution 180° 6. 180° 7. %3D 10. MLABC = 90° 8. 11. ZABC is right angle Multiplication Property of Equality 12. MLABC = M<DAB = MLADC = MLBCD 9. 13. ABCD is a rectangle 10. Choose your answer below. Write the LETTER of your answer on the REASON Column. A. Consecutive angles of a parallelogram are supplementary B. Opposite sides of a parallelogram are congruent C. Opposite angles of a parallelogram are congruent D. Substitution and closure E. Reflexive F. Corresponding Parts of Congruent Triangles are Congruent (CPCTC) G. Side-Side-Side Triangle Congruence (SSS) H. Definition of rectangle I. Definition of right angles J. Transitive
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