Question

1. quadrilateral abcd is similar to quadrilateral abcd. write 2 equations that could be used to solve for missing lengths.

Explanation:

Step1: Recall Similar Figures Property

For similar quadrilaterals, corresponding sides are proportional. Let the sides of \(ABCD\) be \(AB, BC, CD, DA\) and sides of \(A'B'C'D'\) be \(A'B', B'C', C'D', D'A'\). So, \(\frac{AB}{A'B'}=\frac{BC}{B'C'}\) and \(\frac{BC}{B'C'}=\frac{CD}{C'D'}\) (or other pairs of corresponding sides).

Step2: Formulate Equations

Using the proportionality of corresponding sides, two possible equations are:

1. If \(AB\) corresponds to \(A'B'\) and \(BC\) corresponds to \(B'C'\), then \(\frac{AB}{A'B'}=\frac{BC}{B'C'}\).
2. If \(BC\) corresponds to \(B'C'\) and \(CD\) corresponds to \(C'D'\), then \(\frac{BC}{B'C'}=\frac{CD}{C'D'}\). (Or other valid pairs like \(\frac{CD}{C'D'}=\frac{DA}{D'A'}\), \(\frac{DA}{D'A'}=\frac{AB}{A'B'}\) etc.)

Answer:

Two possible equations are \(\boldsymbol{\frac{AB}{A'B'}=\frac{BC}{B'C'}}\) and \(\boldsymbol{\frac{BC}{B'C'}=\frac{CD}{C'D'}}\) (or other valid proportionality equations of corresponding sides of the similar quadrilaterals).