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)
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,...
icon
Related questions
Question
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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education