In the diagram, ABCD is a square with four congruent sides and four right angles. R, S, T, and U are the midpoints of the sides of ABCD. Also, RT ISU and SV= VU. R Prove: A BSR is congruent to A DUT
In the diagram, ABCD is a square with four congruent sides and four right angles. R, S, T, and U are the midpoints of the sides of ABCD. Also, RT ISU and SV= VU. R Prove: A BSR is congruent to A DUT
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.4: Basic Constructions Justified
Problem 38E
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![2DU = DA
2BR = BA
2DT = DC
Substitution Property
2BS 2DU
2BR = 2DT
Division Property
7)
8)
Definition Property of Congruence Segments
Segment BS is congruent to segment DU
Segment BR is congruent to Segment DT
Right Angles Congruence Theorem
9)
Angle B is congruent Angle D
10)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79dec73d-6775-4c21-9728-a233f4ce9792%2Fc35c4cba-e714-4f0f-8646-a866ce0b79fe%2Fh7av69f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2DU = DA
2BR = BA
2DT = DC
Substitution Property
2BS 2DU
2BR = 2DT
Division Property
7)
8)
Definition Property of Congruence Segments
Segment BS is congruent to segment DU
Segment BR is congruent to Segment DT
Right Angles Congruence Theorem
9)
Angle B is congruent Angle D
10)
![C
In the diagram, ABCD is a square with four congruent
sides and four right angles. R, S, T, and U are the
midpoints of the sides of ABCD. Also, RT I SU and
V
SV= VU.
A
Prove: A BSR is congruent to A DUT
田
Statement
Reason
1)
The sides of ABCD are congruent, R, S, T, and
U are midpoints of the sides ABCD; angle B
and angle D are right angles.
2)
Definition of Segment Congruence
3)
BS = SC
DU = UA
BR = RA
DT = TC
4)
Segment Addition Postulate
5)
2BS = BC
2DU = DA
2BR = BA
2DT = DC
Substitution Property
6)
2BS = 2DU
2BR = 2DT](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79dec73d-6775-4c21-9728-a233f4ce9792%2Fc35c4cba-e714-4f0f-8646-a866ce0b79fe%2F9h1olxs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:C
In the diagram, ABCD is a square with four congruent
sides and four right angles. R, S, T, and U are the
midpoints of the sides of ABCD. Also, RT I SU and
V
SV= VU.
A
Prove: A BSR is congruent to A DUT
田
Statement
Reason
1)
The sides of ABCD are congruent, R, S, T, and
U are midpoints of the sides ABCD; angle B
and angle D are right angles.
2)
Definition of Segment Congruence
3)
BS = SC
DU = UA
BR = RA
DT = TC
4)
Segment Addition Postulate
5)
2BS = BC
2DU = DA
2BR = BA
2DT = DC
Substitution Property
6)
2BS = 2DU
2BR = 2DT
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