Question

Write a coordinate proof for the following theorem below. Include the given and prove statements.

If a quadrilateral is a square, then its diagonals are congruent.

Square ABCD and its diagonals have been drawn for you.

Answer 1

Given:square ABCD with diagonals AC and BD and vertices A(0,a), B(c,a), C(c,0), D(0,0)
Prove; AC is congruent to BD
1. ABCD is a square and has diagonals AC and BD and 1. Given
vertices A(0a,),B(c,a), C(c,0), D(0,0)
2.AC=sqrt[(c-0)^2+(a-0)^2]=sqrt(c^2+a^2) 2. Distance Formula
3. BD= sqrt[(c-0)^2+(a-0)^2]=sqrt(a^2+c^2) 3. Distance Formula
4. AC=BD 4. Transitive Prop of Equality
5 AC is congruent to BD 5. Definition of Congruent segments

Answer 2

OMG! Your a savior!:)