Question

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

Right triangle BCA with sides of length a, b, and c. Perpendicular CD forms right triangles BDC and CDA. CD measures h units, BD measures y units, DA measures x units.

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


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


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

Pythagorean Theorum since that is what you are trying to prove.

Answer 2

Answer: Pythagorean Theorem is not the justification for the proof.

Step-by-step explanation:

We can get the right answer with help of the below proof of Pythagoras theorem,

Since, Here ABC is the triangle in which CD is the altitude from the point C.

Where,  $D\in AB$ ( shown in figure)

Here, segment BC = a, segment CA = b, segment AB = c, segment CD = h

segment DB = y , segment AD = x  

y + x = c ( c over a equals a over y and c over b equals b over x)

Since, $\triangle ABC\sim \triangle ACD$ ⇒ a/c=y/a and $\triangle ABC\sim \triangle BCD$⇒  b/x=c/b ( Pieces of Right Triangles Similarity Theorem)

⇒ a^2=cy and b^2=cx  (  Cross Product Property)

$a^2 + b^2 = cy + b2$ (Addition Property of Equality)

$a^2 + b^2 = cy + cx$  

$a^2 + b^2 = c(y + x)$  

$a^2 + b^2 = c(c)$

$a^2 + b^2 = c^2$