Fill in the missing statement and reason of the proof below. Given: ABCD is a rhombus and AE BE. Prove: ABCD is a square. Step Statement Reason ABCD is a rhombus Given AE BE AC and BD bisect each other The diagonals of a rhombus bisect each other When a segment is bisected, the whole segment is twice the length of each part AC = 2AE Type of Statement AC BD Segments that are twice the lengths of congruent segments are congruent ABCD is a square ABCD is a square because it is a rhombus with congruent diagonals A E B Note: AC and BD are segments. 1. 2. 4.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 46E
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solve/12993350/quadProofsOneMissingStep
Fill in the missing statement and reason of the proof below.
Given: ABCD is a rhombus and AE BE.
Prove: ABCD is a square.
Step
Statement
Reason
ABCD is a rhombus
Given
AE BE
AC and BD bisect each other
The diagonals of a rhombus bisect each other
When a segment is bisected, the whole segment is twice the length
of each part
3
AC = 2AE
4
Type of Statement
AC BD
Segments that are twice the lengths of congruent segments are
congruent
ABCD is a square because it is a rhombus with congruent
diagonals
ABCD is a square
E
C
Note: AC and BD are segments.
You must answer all questions above in order to submit.
attempt i out of 2
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Transcribed Image Text:solve/12993350/quadProofsOneMissingStep Fill in the missing statement and reason of the proof below. Given: ABCD is a rhombus and AE BE. Prove: ABCD is a square. Step Statement Reason ABCD is a rhombus Given AE BE AC and BD bisect each other The diagonals of a rhombus bisect each other When a segment is bisected, the whole segment is twice the length of each part 3 AC = 2AE 4 Type of Statement AC BD Segments that are twice the lengths of congruent segments are congruent ABCD is a square because it is a rhombus with congruent diagonals ABCD is a square E C Note: AC and BD are segments. You must answer all questions above in order to submit. attempt i out of 2 Privacy Policy Terms of Service
Step
Statement
Reason
ABCD is a rhombus
Given
1
AE BE
AC and BD bisect each other
The diagonals of a rhombus bisect each othe
When a segment is bisected, the whole segm
of each part
AC = 2AE
4
Type of Statement
XY WZ
Segments that are twice the lengths of congri
congruent
ZX ZY
ABCD is a square because it is a rhombus u
6.
diagonals
ΔΧΥΖ -ΔΤUV
XY WZ
D
XY 1WZ
Classify a triangle
Classify a quadrilateral
ZX and ZY are
complementary/supplementary
ZX is a right angle
XY bisects ZX
XY bisects W Z
XY WZ (or 2W Z)
%3D
AC and BD are segments.
mZX = mZY (or 2mZY)
%3D
You must answer all questions above in order to submit.
Transcribed Image Text:Step Statement Reason ABCD is a rhombus Given 1 AE BE AC and BD bisect each other The diagonals of a rhombus bisect each othe When a segment is bisected, the whole segm of each part AC = 2AE 4 Type of Statement XY WZ Segments that are twice the lengths of congri congruent ZX ZY ABCD is a square because it is a rhombus u 6. diagonals ΔΧΥΖ -ΔΤUV XY WZ D XY 1WZ Classify a triangle Classify a quadrilateral ZX and ZY are complementary/supplementary ZX is a right angle XY bisects ZX XY bisects W Z XY WZ (or 2W Z) %3D AC and BD are segments. mZX = mZY (or 2mZY) %3D You must answer all questions above in order to submit.
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ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage