"To determine:Whether each pair of figures is similar..." was answered by our experts

High School
Geometry
High school geometry
Similarity

floymdiT

Answered question

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.

Answer & Explanation

Faiza Fuller

Skilled2020-12-07Added 108 answers

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 $∠ Y and ∠ B$ are right angles.
Therefore,
$∠ Y \tilde{=} ∠ B$

The ratio of corresponding sides
$\frac{X Y}{A B} = \frac{4}{14}$
$= \frac{2}{7}$
And,
$\frac{Y Z}{B C} = \frac{7}{24.5}$
$= \frac{2}{7}$
So, $\frac{X Y}{A B} = \frac{Y Z}{B C} = \frac{2}{7}$
Therefore, $△ X Y Z \sim △ A B C$ by SAS similarity theorem and the scale factor is $\frac{2}{7}$ .

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