(1) Prove: If AB = 5x, BC = 2x –4, and AC = 52, then x = 8.

Question

(2) Prove: If AB = CD, then AC = BD.

Answer 1

1. AB + BC = AC.
5x + (2x-4) = 52.
7x = 52 + 4 = 56,
X = 8.

2. AB + BC = AC: Addition.
BC + CD = BD: Addition.
AB = CD: Given.
Therefore, AB + BC = BD: Substitution.
AC = BD: Quantitives that are = to the same quantitive are = to each other.