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 are similar (given \(\triangle WVU \sim \triangle WED\)), so corresponding sides are proportional. Let the missing length be \(x\) (side \(WE\) or corresponding). The sides \(WV = 104 + 27 = 131\)? Wait, no—wait, \(\triangle WVU \sim \triangle WED\), so the ratio of corresponding sides: \(WV/WD = WU/WE\)? Wait, looking at the diagram, \(WV = 104\), \(WD = 27\), \(WU = 117\), and \(WE = x\)? Wait, no, maybe \(WV/WD = WU/WE\)? Wait, the user's work shows \(\frac{104}{27}=\frac{117}{x}\)? Wait, no, cross - multiply: \(104x = 117\times27\)? Wait, no, maybe the correct proportion is from similar triangles: \(\triangle WVU \sim \triangle WED\), so \(\frac{WV}{WE}=\frac{WU}{WD}\)? Wait, no, let's re - examine. The triangles are similar, so corresponding sides: \(WV\) corresponds to \(WE\), \(WU\) corresponds to \(WD\), \(VU\) corresponds to \(ED\). Wait, the user's calculation: \(104\times27 = 2808\), then \(2808\div117 = 24\). Let's check: If \(\frac{WV}{WE}=\frac{WU}{WD}\), then \(WV = 104\), \(WE=x\), \(WU = 117\), \(WD = 27\). So \(\frac{104}{x}=\frac{117}{27}\), cross - multiply: \(117x=104\times27\), \(x=\frac{104\times27}{117}\). Simplify: \(104 = 8\times13\), \(27 = 3\times9\), \(117 = 9\times13\). So \(x=\frac{8\times13\times3\times9}{9\times13}=24\).

Step2: Verify the Proportion

Using the property of similar triangles (corresponding sides are proportional), we set up the proportion based on the corresponding sides of \(\triangle WVU\) and \(\triangle WED\). After cross - multiplying and simplifying the fraction, we get the value of the missing length.

Answer:

The missing length is \(24\).