Complete the Given: Square ABCD with diagonals AC and BD Prove: AC 1 BD Statements Reasons 1. (1) Given CB CD 3. (3) 2. (2) The diagonals of a parallelogram bisect each other. Definition of a midpoint D. 4. E is the midpoint of AC and BD 5. CE CE 6. ADCE ABCE 7. LDEC LBEC 8. (4) RS 1 OE E Reflexive Property SSS Postulate СРСТС (5) Pernendicular lines meet to form a right angle 9.
Complete the Given: Square ABCD with diagonals AC and BD Prove: AC 1 BD Statements Reasons 1. (1) Given CB CD 3. (3) 2. (2) The diagonals of a parallelogram bisect each other. Definition of a midpoint D. 4. E is the midpoint of AC and BD 5. CE CE 6. ADCE ABCE 7. LDEC LBEC 8. (4) RS 1 OE E Reflexive Property SSS Postulate СРСТС (5) Pernendicular lines meet to form a right angle 9.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question

Transcribed Image Text:Properties of Rhombus
Diagonals of a rhombus are perpendicular.
Given: Rhombus ROSE with
diagonals RS and OE
Prove: RS 1 DE
Statements
1.
Reasons
Rhombus ROSE diagonals
RS and OE
OS = RO
3. RS and OE bisect each
other
Given
R.
2.
Definition of a Rhombus
The diagonals of a
parallelogram bisect each
other.
4.
His the midpoint of RS and
Definition of a midpoint
OE
Reflexive Property
SSS Postulate
СРСТС
5.
6. AROH ASOH
HO HO
ZRHO LSHO
ZRHO and SHO are right
7.
8.
angles
RS 1OE
ZRHO and SH0 form a linear
pair and are congruent
Perpendicular lines meet to
form a right angle
9.
Each diagonal of a rhombus bisects opposite angles.
Given: Rhombus VWXY with
Reasons
Given
Statements
diagonals VX and WY
Prove: 21 e 42 and 43 4
Rhombus VWXY with
diagonals VX and WY
2. YV VW and WX = XY
Definition of a Rhombus
Reflexive Property
SSS Postulate
СРСТС
3.
WY YW
4.
AYVW E AW XY
5.
21 42 and 23 4
X,
Learning Task 1
Complete the two-column proof to prove the following
Given: Square ABCD with
diagonals AC and BD
Prove: AC BD
Statements
Reasons
(1)
2. CB CD
3.
Given
(2)
The diagonals of a
parallelogram bisect each
other.
Definition of a midpoint
(3)
4. E is the midpoint of AC and
BD
Reflexive Property
SSS Postulate
СРСТС
(5)
Pernendicular lines meet to
form a right angle
5.
CE CE
ADCE ABCE
6.
ZDEC LBEC
8.
7.
(4)
RS 1OE
9.
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