Question

1. given that \\( \triangle fun \sim \triangle dog \\), which angle is congruent to \\( \angle o \\).

(1) \\( \angle d \\)
(2) \\( \angle o \\)
(3) \\( \angle g \\)
(4) \\( \angle n \\)

1. the ratio of a pair of corresponding sides of similar pentagons is \\( 3:4 \\). find the ratio of their perimeters.

(1) \\( 3:4 \\)
(2) \\( 6:8 \\)
(3) \\( 9:16 \\)
(4) \\( 9:12 \\)

1. in the diagram of \\( \triangle adc \\) below, \\( \overline{eb} \parallel \overline{dc} \\), \\( ae = 9 \\), \\( ed = 5 \\), and \\( ab = 9.2 \\). what is the length of \\( \overline{ac} \\), to the

nearest tenth?
(1) 5.1
(2) 5.2
(3) 14.3
(4) 14.4

1. if \\( \triangle opq \sim \triangle rst \\) with \\( op = 7 \\), \\( qp = 5 \\), and \\( ts = 22 \\), find the length of \\( \overline{rs} \\). round your answer

to the nearest tenth.
(1) 1.6
(2) 14.0
(3) 15.7
(4) 30.8

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \(EB\parallel DC\) in \(\triangle ADC\), by the basic proportionality theorem, \(\frac{AE}{ED}=\frac{AB}{BC}\).
Given \(AE = 9\), \(ED = 5\), and \(AB=9.2\). Let \(BC=x\). Then \(\frac{9}{5}=\frac{9.2}{x}\).
Cross - multiply: \(9x=9.2\times5\).
So \(9x = 46\), and \(x=\frac{46}{9}\approx5.1\).

Step2: Calculate the length of \(AC\)

\(AC=AB + BC\).
Substitute \(AB = 9.2\) and \(BC\approx5.1\).
\(AC=9.2+5.1 = 14.3\).

Answer:

(3) \(14.3\)