MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

Answer: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 justificationLet segment BC = a, segment CA = b ,segment AB = c segment CD = h, segment DB = x, segment AD = y ,y + x = cIn 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.[tex]\frac{BD}{BC}=\frac{BC}{BA}\\\frac{x}{a}=\frac{a}{x}[/tex]⇒ 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)⇒[tex]a^2+ b^2=cx+cy[/tex][tex]a^2+ b^2=c(x+y)[/tex] =c×c [∴ x+y =c] =c²So, 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.