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Guillermo claims that a 2 + b 2 = c 2 for any right triangle with legs a and b and hypotenuse c. He draws the diagram below to use with his proof. Guillermo's proof is shown below. Some of the reasons
Guillermo claims that a
2
+ b
2
= c
2
for any right triangle with legs a and b and hypotenuse c. He
draws the diagram below to use with his proof.
Guillermo's proof is shown below. Some of the reasons are missing from the proof.
Statement Reason
1
∠A ≅ ∠A and
∠B ≅ ∠B
2
∠ACB ≅
∠ADC and
∠ACB ≅
∠CDB
All right angles
are congruent.
3
ΔACB ∼
ΔADC and
ΔACB ∼
ΔCDB
4
a
c
=
d
a
and
b
c
=
e
b
5
a
2
= cd and b
2
= ce
Product of the
means is equal
to the product
of the extremes
6
a
2
+ b
2
= cd +
ce
Addition
property of
equality
7
a
2
+ b
2
= c · (d
+ e)
8 a
2
+ b
2
= c · c
9 a
2
+ b
2
= c
2
Property of
exponents
Select each correct description of the missing reasons in the proof.
A. Reason 1 is the Symmetric Property.
B. Reason 3 is the Angle–Angle criterion.
C. Reason 4 is the proportionality of corresponding sides in similar triangles.
D. Reason 7 is the associative property.
E. Reason 8 is the line segment addition postulate.
