Question

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

1. in the diagram, segment ab is parallel to segment ab. \\(\overline{ab} \parallel \overline{ab}\\)

diagram of triangle with points c, b, a; a and b on ca and cb respectively, with lengths: from c to a to a: 12, 20? from c to b to b: 6, 8?

a. what is the length of segment aa?
b. what is the length of segment bb?

1. in the diagram, lines bc and de are both vertical.

diagram of a line with points a, b, d; vertical lines at b (bc=2) and d (de=5), ab=3

what is the length of ad?
a. 4.5
b. 5
c. 7.5
d. 10

1. triangle def is formed by connecting the midpoints of the sides of triangle abc.

diagram of triangle abc with midpoints d, e, f; lengths: de=2, ef=3, fd=4

select all true statements.
a. triangle bde is congruent to triangle efc.
b. triangle bde is congruent to triangle fda.
c. bd is congruent to fe.
d. the length of bc is 8.
e. the length of bc is 6.

Explanation:

Step1: Identify Similar Figures Property

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

Step2: Verify Proportionality

Since similarity implies equal ratios of corresponding sides, these equations use the fundamental property of similar polygons (proportional corresponding sides) to solve for missing lengths.

Answer:

Two equations are \(\boldsymbol{\frac{AB}{A'B'}=\frac{BC}{B'C'}}\) and \(\boldsymbol{\frac{CD}{C'D'}=\frac{DA}{D'A'}}\) (other valid proportional equations of corresponding sides are also acceptable).