Given that AABC is a triangle with sides of lengths a, b, and c such that c² > a² + b², prove AABC is an obtuse triangle. B C a A B C Draw a right triangle AEFG with legs of lengths a and b. Label the hypotenuse x. Determine what needs to be proved to prove AABC is an obtuse triangle. a Prove: mZC mZG Given that c² > a² + b² use This proves that m/C mZG using A for the AEFG to substitute F a G x [1] E for a² + b² to get
Given that AABC is a triangle with sides of lengths a, b, and c such that c² > a² + b², prove AABC is an obtuse triangle. B C a A B C Draw a right triangle AEFG with legs of lengths a and b. Label the hypotenuse x. Determine what needs to be proved to prove AABC is an obtuse triangle. a Prove: mZC mZG Given that c² > a² + b² use This proves that m/C mZG using A for the AEFG to substitute F a G x [1] E for a² + b² to get
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.4: The Trapezoid
Problem 3E: What type of trapezoid a has congruent diagonals. b has congruent base angles.
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Question
1
![Given that AABC is a triangle with sides of
lengths a, b, and c such that c² > a² + b², prove
AABC is an obtuse triangle.
B
C
a
A
B
C
Draw a right triangle AEFG with legs of lengths a and b. Label the
hypotenuse x. Determine what needs to be proved to prove AABC is
an obtuse triangle.
a
Prove: mZC
mZG
Given that c² > a² + b² use
This proves that m/C
mZG using
A
for the AEFG to substitute
F
a
G
x
[1]
E
for a² + b² to get](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F963f7515-03fc-48e7-b6eb-dd7da14fe76e%2Fbbeee10d-de28-42aa-ba7f-b6b8c404ed91%2Fxuel7mr_processed.png&w=3840&q=75)
Transcribed Image Text:Given that AABC is a triangle with sides of
lengths a, b, and c such that c² > a² + b², prove
AABC is an obtuse triangle.
B
C
a
A
B
C
Draw a right triangle AEFG with legs of lengths a and b. Label the
hypotenuse x. Determine what needs to be proved to prove AABC is
an obtuse triangle.
a
Prove: mZC
mZG
Given that c² > a² + b² use
This proves that m/C
mZG using
A
for the AEFG to substitute
F
a
G
x
[1]
E
for a² + b² to get
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