4.14 Similar Triangles Exercises 4.14 1.)P is any point in arc APB and C is the midpoint of arc ACB. If chord AB cuts chord CP at E, prove that AAPC ~ AEÁC. "Exercise 4.14 #10: If the hypotenuse and a leg of one right triangle are proportional to the hypotenuse and a leg of another, then the two triangles are similar. A4 c' a' T' c' - Given: b b' - Prove: AT ~ AT' Statements Reasons Statements Reasons 1. (see above) 1. Given a2 is b2 5. Subtraction a'2 %| b'2 Transformation 2. If 4 quantities are in proportion, then like powers are in proportion. c2 c'2 a2 b2 6. Alternation %3D b2 b'2 b'2 Transformation 3. c2 = a2 + b2; c'2 = a'2 + b'2 7. If 4 quantitie proportion, the are in proportic b. 3. Pythagorean Theorem b' a' a?+b2 4. b2 a'2+b'2 %3D b'2 4. Substitution (step 3 -> 2) 9. AT ~ AT' 9. 1.1. 6. 7. 2.

Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter5: Similar Triangles
Section5.6: Segments Divided Proportionally
Problem 36E
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Please answer in a two-column proof.

The question is in the picture. Also, there is an example of how it should look like/how it should be done in the second picture. (Note: THERE SHOULD BE *ONLY* ONE GIVEN (statement))

4.14 Similar Triangles
Exercises 4.14
1.)P is any point in arc APB and C is the
midpoint of arc ACB. If chord AB cuts
chord CP at E, prove that AAPC ~ AEÁC.
Transcribed Image Text:4.14 Similar Triangles Exercises 4.14 1.)P is any point in arc APB and C is the midpoint of arc ACB. If chord AB cuts chord CP at E, prove that AAPC ~ AEÁC.
"Exercise 4.14 #10: If the hypotenuse and a
leg of one right triangle are proportional to
the hypotenuse and a leg of another, then
the two triangles are similar.
A4
c'
a'
T'
c'
- Given:
b
b'
- Prove: AT ~ AT'
Statements
Reasons
Statements
Reasons
1. (see above)
1. Given
a2
is
b2
5. Subtraction
a'2
%|
b'2
Transformation
2. If 4 quantities are in
proportion, then like
powers are in proportion.
c2
c'2
a2
b2
6. Alternation
%3D
b2
b'2
b'2
Transformation
3. c2 = a2 + b2;
c'2 = a'2 + b'2
7. If 4 quantitie
proportion, the
are in proportic
b.
3. Pythagorean Theorem
b'
a'
a?+b2
4.
b2
a'2+b'2
%3D
b'2
4. Substitution (step 3 -> 2) 9. AT ~ AT'
9. 1.1.
6.
7.
2.
Transcribed Image Text:"Exercise 4.14 #10: If the hypotenuse and a leg of one right triangle are proportional to the hypotenuse and a leg of another, then the two triangles are similar. A4 c' a' T' c' - Given: b b' - Prove: AT ~ AT' Statements Reasons Statements Reasons 1. (see above) 1. Given a2 is b2 5. Subtraction a'2 %| b'2 Transformation 2. If 4 quantities are in proportion, then like powers are in proportion. c2 c'2 a2 b2 6. Alternation %3D b2 b'2 b'2 Transformation 3. c2 = a2 + b2; c'2 = a'2 + b'2 7. If 4 quantitie proportion, the are in proportic b. 3. Pythagorean Theorem b' a' a?+b2 4. b2 a'2+b'2 %3D b'2 4. Substitution (step 3 -> 2) 9. AT ~ AT' 9. 1.1. 6. 7. 2.
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