Properties of RhombusDiagonals of a rhombus are perpendicular.Given: Rhombus ROSE withdiagonals RS and OEProve: RS 1 DEStatements1.ReasonsRhombus ROSE diagonalsRS and OEOS = RO3. RS and OE bisect eachotherGivenR.2.Definition of a RhombusThe diagonals of aparallelogram bisect eachother.4.His the midpoint of RS andDefinition of a midpointOEReflexive PropertySSS PostulateСРСТС5.6. AROH ASOHHO HOZRHO LSHOZRHO and SHO are right7.8.anglesRS 1OEZRHO and SH0 form a linearpair and are congruentPerpendicular lines meet toform a right angle9.Each diagonal of a rhombus bisects opposite angles.Given: Rhombus VWXY withReasonsGivenStatementsdiagonals VX and WYProve: 21 e 42 and 43 4Rhombus VWXY withdiagonals VX and WY2. YV VW and WX = XYDefinition of a RhombusReflexive PropertySSS PostulateСРСТС3.WY YW4.AYVW E AW XY5.21 42 and 23 4X,Learning Task 1Complete the two-column proof to prove the followingGiven: Square ABCD withdiagonals AC and BDProve: AC BDStatementsReasons(1)2. CB CD3.Given(2)The diagonals of aparallelogram bisect eachother.Definition of a midpoint(3)4. E is the midpoint of AC andBDReflexive PropertySSS PostulateСРСТС(5)Pernendicular lines meet toform a right angle5.CE CEADCE ABCE6.ZDEC LBEC8.7.(4)RS 1OE9.

Statement Reason 1. (1) Square ABCD with diagonals AC¯ and BD¯. Given

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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Concept explainers

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

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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