Question

To determine:Whether each pair of figures is similar and also write similarity statement and scale factor.Given information:Given the figure.12210203002.jpg

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ANSWERED
asked 2020-12-06

To determine:Whether each pair of figures is similar and also write similarity statement and scale factor.
Given information:
Given the figure.
image

Expert Answers (1)

2020-12-07

Calculation:
When the lenght of the triangles are proportional to the lenght of two corresponding sides of another triangle and the included angles are congruent.
So, the triangles are similar by SAS similarity theorem.
Given that \(\displaystyle\angle{Y}{\quad\text{and}\quad}\angle{B}\) are right angles.
Therefore,
\(\displaystyle\angle{Y}\stackrel{\sim}{=}\angle{B}\)
image
The ratio of corresponding sides
\(\displaystyle\frac{{{X}{Y}}}{{{A}{B}}}=\frac{{4}}{{14}}\)
\(\displaystyle=\frac{{2}}{{7}}\)
And,
\(\displaystyle\frac{{{Y}{Z}}}{{{B}{C}}}=\frac{{7}}{{24.5}}\)
\(\displaystyle=\frac{{2}}{{7}}\)
So, \(\displaystyle\frac{{{X}{Y}}}{{{A}{B}}}=\frac{{{Y}{Z}}}{{{B}{C}}}=\frac{{2}}{{7}}\)
Therefore, \(\displaystyle\triangle{X}{Y}{Z}\sim\triangle{A}{B}{C}\) by SAS similarity theorem and the scale factor is \(\displaystyle\frac{{2}}{{7}}\).

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