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
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter6: Circles
Section6.3: Line And Segment Relationships In The Circle
Problem 39E: The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle...
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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
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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