Use the following diagram and information to complete the proof. Given: ABCD is a parallelogram with congruent diagonals. Prove: ABCD is a rectangle. D 0 2016 StrongMind. Created using GeoGebra. Match each numbered statement with the correct reason to complete the proof

Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 23E
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Use the following diagram and information to complete the proof.
Given: ABCD is a parallelogram with congruent diagonals.
Prove: ABCD is a rectangle.
O DASHBOARD
D
I COURSES
E CALENDAR
O 2016 StrongMind. Created using GeoGebra.
Match each numbered statement with the correct reason to
INBOX
complete the proof.
1. ABCD is a parallelogram.
AC BD
( НELP
2. AB DC
3. AD AD
4. AABD ADCA
5. ZBAD ZCDA
6. MZBAD = M2CDA
7.
m/BAD+ MLCDA = 180°
m/DCB+ m/CBA = 180
m/BAD + m/BAD = 180°
9. 2(m/BAD) = 180°
10. MZBAD =90"
11. ABCD is a rectangle.
: Given
: Reflexive Property of Congruence
: SSS Congruence Postulate
Corresponding parts of congruent triangles are
congruent.
: Definition of congruent angles
Consecutive angles of a parallelogram are
supplementary.
: Substitution Property of Equality
* Addition
: Division Property of Equality
: Definition of a rectangle
: Consecutive angles of a parallelogram are congruent.
: SAS Congruence Postulate
: Opposite sides of a parallelogram are congruent.
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Transcribed Image Text:Use the following diagram and information to complete the proof. Given: ABCD is a parallelogram with congruent diagonals. Prove: ABCD is a rectangle. O DASHBOARD D I COURSES E CALENDAR O 2016 StrongMind. Created using GeoGebra. Match each numbered statement with the correct reason to INBOX complete the proof. 1. ABCD is a parallelogram. AC BD ( НELP 2. AB DC 3. AD AD 4. AABD ADCA 5. ZBAD ZCDA 6. MZBAD = M2CDA 7. m/BAD+ MLCDA = 180° m/DCB+ m/CBA = 180 m/BAD + m/BAD = 180° 9. 2(m/BAD) = 180° 10. MZBAD =90" 11. ABCD is a rectangle. : Given : Reflexive Property of Congruence : SSS Congruence Postulate Corresponding parts of congruent triangles are congruent. : Definition of congruent angles Consecutive angles of a parallelogram are supplementary. : Substitution Property of Equality * Addition : Division Property of Equality : Definition of a rectangle : Consecutive angles of a parallelogram are congruent. : SAS Congruence Postulate : Opposite sides of a parallelogram are congruent. 回 日 画
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