/7. ABC and DEF are two isosceles trian- gles on bases BC and EF respectively. If AB : BC = DE : EF, prove that the two triangles are similar. %3D "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.

/7. ABC and DEF are two isosceles trian- gles on bases BC and EF respectively. If AB : BC = DE : EF, prove that the two triangles are similar. %3D "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, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.2: Pyramids, Area, And Volume

Problem 14E: Refer to the prisms of Exercises 1 and 2. Which of these have symmetry with respect to one or more...

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