Question

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

Answer: Pythagorean Theorem Pieces of Right Triangles is not a justification for the proof.

Explanation : Here, $\triangle ABC$ is a right triangle with sides a, b and c. Perpendicular CD forms right triangles BDC and CDA.

CD measures h units, BD measures y units, DA measures x units.

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

a/c=y/a( Similarity theorem in triangles ABC and DBC )

$a^2 = cy$------(1) (Cross Product Property)

Similarly, $b^2 = cx$ (Similarity theorem in triangles ABC and ADC)---------(2)

$a^2 + b^2 = cy + cx$(after adding equation (1) and (2) )

$a^2 + b^2 = c(y + x)$( By additional property of equality)

$a^2 + b^2 = c^2$. ( because y + x=c)

Thus, it has been proved that except Pythagorean Theorem Pieces of Right Triangles we use all other properties.

Answer 2

Answer:

The answer is B (Pythagorean Theorem)

Step-by-step explanation:

I just took the test and got the answer right

Proof is right here: