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, B

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? (5 points)

Group of answer choices

Substitution

Addition Property of Equality

Transitive Property of Equality

Distributive Property of Equality

Question

12-07-2022
Mathematics

contestada

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, B

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? (5 points)

Group of answer choices

Substitution

Addition Property of Equality

Transitive Property of Equality

Distributive Property of Equality

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akposevictor akposevictor · Answer 1 · 2022-07-13T20:59:20+02:00

The property that is not a justification for the proof is: B. addition property of equality.

What is the Addition Property of Equality?

According to the addition property of equality, if a - b = c, then a - b + b = c + b, which is: a = c + b.

In the proof given, there is no single statement that shows that we are adding a figure or variable to both sides of any equation, therefore, the justification that is not part of the proof is: addition property of equality.

Learn more about addition property of equality on:

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