Question

unit 4 test remediation
state if the two triangles are congruent. if they are, state by which congruence theorem.
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state if the two triangles are similar. if they are, state by which similarity theorem.
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find the missing length. the triangles in each pair are similar.
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△wvu ~ △wed

Explanation:

Step1: Identify Similar Triangles

The triangles \(\triangle SRI\) and \(\triangle BRC\) are similar (by AA similarity, as they share a right angle and a common angle at \(R\)). So, their corresponding sides are proportional.

Step2: Set Up Proportion

Let the missing length (height of \(\triangle BRC\)) be \(x\). The sides of \(\triangle SRI\) are \(12\) (height), \(9\) (base), and \(\triangle BRC\) has base \(6\) and height \(x\). The proportion is \(\frac{x}{12}=\frac{6}{9}\).

Step3: Solve for \(x\)

Cross - multiply: \(9x = 12\times6\). Then \(9x=72\), and \(x=\frac{72}{9}=8\).

Answer:

The missing length is \(8\).