Question

Given: ∆BCA is a right triangle.
Prove: a2 + b2 = c2


The two-column proof with missing justifications proves the Pythagorean Theorem using similar triangles.

Statement Justification
Draw an altitude from point C to
Let = a
= b
= c
= h
= x
= y
y + x = c

a2 = cy; b2 = cx
a2 + b2 = cy + b2
a2 + b2 = cy + cx
a2 + b2 = c(y + x)
a2 + b2 = c(c)
a2 + b2 = c2


Which is NOT a justification for the proof?

Addition Property of Equality

Pythagorean Theorem

Pieces of Right Triangles Similarity Theorem

Cross Product Property

Answer 1

Statement Justification
Draw an altitude from point C to
Let segment BC = a
segment CA= b
segment AB= c
segment CD= h
segment DB= x
segmet AD= y
y + x = c

c over a = a over y , c over b = b over x

a2 = cy; b2 = cx
a2 + b2 = cy + b2
a2 + b2 = cy + cx
a2 + b2 = c(y + x)
a2 + b2 = c(c)
a2 + b2 = c2

Answer 2

^^^^^^^^^^^ better version of second half of the question

Answer 3

@SmoothMath ?

Answer 4

@robtobey ?

Answer 5

@jim_thompson5910

Answer 6

which one do you think it is

Answer 7

pythagorean was my guess, to be honest all of them seemed like they could be the answer, it has me very confused

Answer 8

you are correct, you're trying to prove the pythagorean theorem so there's no way you can use something you're trying to prove as justification (that would be using circular reasoning)

Answer 9

okay thank you very much (:

Answer 10

np