In the following triangle, point E is the midpoint of AB, and point D is the midpoint of AC. D E Below is the proof that DE = CB. The proof is divided into four parts, where the title of each part indicates its main purpose. Complete part D of the proof. DE СА Part A: Prove = 2 Pick ratio v %3D DA [Show the steps.] V Pick ratio BA = 2 EA Part B: Prove (CD)/(DA) [Show the steps.] (CA)/(DA) Part C: Prove AC AB ~ ADAE [Show the steps.] (CA)/(CD) =CB Part D: Prove DE = СВ
In the following triangle, point E is the midpoint of AB, and point D is the midpoint of AC. D E Below is the proof that DE = CB. The proof is divided into four parts, where the title of each part indicates its main purpose. Complete part D of the proof. DE СА Part A: Prove = 2 Pick ratio v %3D DA [Show the steps.] V Pick ratio BA = 2 EA Part B: Prove (CD)/(DA) [Show the steps.] (CA)/(DA) Part C: Prove AC AB ~ ADAE [Show the steps.] (CA)/(CD) =CB Part D: Prove DE = СВ
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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![In the following triangle, point E is the midpoint of AB, and point D is the midpoint of AC.
B
E
A
1
CB. The proof is divided into four parts, where the title of each part
2
Below is the proof that DE =
indicates its main purpose.
Complete part D of the proof.
DE
CA
= 2
DA
Part A: Prove
Pick ratio v
[Show the steps.]
V Pick ratio
ВА
Part B: Prove
EA
(CD)/(DA)
[Show the steps.]
(CA)/(DA)
Part C: Prove ACAB ~ ADAE
[Show the steps.]
(CA)/(CD)
CB
Part D: Prove DE=
СВ
Statement
Reason
CB
Lengths of corresponding sides of similar triangles have equal ratios.
(Part C)
12
DE
Pick ratio v
CB
13
Substitution (Part A, 12)
DE
14
CB=DE
Multiply both sides of the equation by
Pick expression v
(13)
n by
Pick expression
v Pick expression
2.DE
oble
DE
(DE)/2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdeb7629a-098d-4da5-9bd3-72a628602cc4%2Fa059f814-1fc5-4927-a91c-da6c7cf23b24%2Fevujcdf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the following triangle, point E is the midpoint of AB, and point D is the midpoint of AC.
B
E
A
1
CB. The proof is divided into four parts, where the title of each part
2
Below is the proof that DE =
indicates its main purpose.
Complete part D of the proof.
DE
CA
= 2
DA
Part A: Prove
Pick ratio v
[Show the steps.]
V Pick ratio
ВА
Part B: Prove
EA
(CD)/(DA)
[Show the steps.]
(CA)/(DA)
Part C: Prove ACAB ~ ADAE
[Show the steps.]
(CA)/(CD)
CB
Part D: Prove DE=
СВ
Statement
Reason
CB
Lengths of corresponding sides of similar triangles have equal ratios.
(Part C)
12
DE
Pick ratio v
CB
13
Substitution (Part A, 12)
DE
14
CB=DE
Multiply both sides of the equation by
Pick expression v
(13)
n by
Pick expression
v Pick expression
2.DE
oble
DE
(DE)/2
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