Chapter P - P.2 - Linear Models and Rates of Change - Exercises - Page 18: 89

1, $AB ≅ BC$ All sides of a rhombus are congruent 2. $AE ≅ EC$ Since a rhombus is a parallelogram, its diagonals bisect each other 3. $BE ≅ BE$ All sides are congruent to themselves 4. $ΔAEB ≅ ΔCEB$ Side-side-side congruence 5. $∠AEB ≅ ∠CEB$ Corresponding angles are congruent 6. $∠AEB$ and $∠CEB$ are supplementary angles 7. $EB ⟂ AC$ since the angles formed are supplementary and congruent Therefore the diagonals of a rhombus intersect at right angles

First, we can prove that the triangles created by the diagonals of the rhombus are congruent using information we already know about a rhombus. After that we can prove that the diagonals intersect at right angles.