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 = x segment ad = y 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? pieces of right triangles similarity theorem side-side-side similarity theorem substitution addition property of equality

There is a misprint in the question.

In the statement you have written DB=x ,and DA=y but in Question you have written DA= x and DB=y.

So, let me just considering your Statement justification

Let segment BC = a, segment CA = b ,segment AB = c segment CD = h, segment DB = x, segment AD = y ,y + x = c

In Δ B DC and Δ BC A

∠B D C =∠B C A [each being 90°]

∠ B is common.

Δ B D C is similar to Δ BC A.

⇒ a² = c x  .........(1)

Similarly we can prove that

Δ ADC is similar to Δ BC A.

⇒b²= c y ......(2)

adding (1) and (2)

⇒

               =c×c [∴ x+y =c]

                 =c²

So, we have used two properties 1.  Right Triangles Similarity Theorem 2.Substitution Addition Property of Equality.

we haven't used  Side-Side-Side Similarity Theorem. It is not the right justification for the proof.

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.