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 proves the pythagorean theorem using similar triangles. statement justification draw an altitude from point c to line segment ab by construction let segment bc = a segment ca = b segment ab = c segment cd = h segment db = y segment ad = x by labeling y x = c segment addition postulate c over a equals a over y and c over b equals b over x pieces of right triangles similarity theorem a2 = cy; b2 = cx cross product property a2 b2 = cy b2 addition property of equality a2 b2 = cy cx substitution a2 b2 = c(y x) ? a2 b2 = c(c) substitution a2 b2 = c2 multiplication which of the following is the missing justification in the proof? addition property of equality distributive property of equality transitive property of equality cross product property

Answer 1

The missing justification in the proof is the Transitive Property of Equality.

Step-by-step explanation:

The missing justification in the proof is the Transitive Property of Equality.

1. A right triangle ABC is given, where BC = a, AC = b, and AB = c.
2. An altitude CD is drawn from point C to line segment AB, creating two right triangles BDC and CDA.
3. The length of CD is h units, BD is y units, and AD is x units.
4. Using the Segment Addition Postulate, we have c/a = a/y and c/b = b/x.
5. By applying the Pieces of Right Triangles Similarity Theorem, we obtain a² = cy and b² = cx.
6. Using the Cross Product Property, we can rewrite this as a²b² = cy·cx.
7. Using the missing justification, the Transitive Property of Equality, we have a²b² = c².
8. Finally, by using the Multiplication Property of Equality, we have a²b² = c².