Question
Pimilar Palygons T. Thangle DEF is a dilation of triangle ABC with scale factor 2 . In triangle ABC, the largest angle measures \( 82^{\circ} \). What is the largest angle measure in triangle DEF? \( \begin{array}{ll}\text { (A) } 41 & \text { (C) } 123^{\circ} \\ \begin{array}{ll}\text { B. } 82^{\circ} & \text { (D) } 164^{\circ}\end{array}\end{array} \)
Ask by Donnelly Hammond. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The largest angle in triangle DEF is \(82^\circ\).
Solution
In similar triangles, such as triangle DEF being a dilation of triangle ABC with a scale factor of 2, the corresponding angles remain **unchanged**. Dilation affects the size of the sides but does not alter the measure of the angles.
Given that the largest angle in triangle ABC is \(82^\circ\), the largest angle in triangle DEF will also be:
**\(82^\circ\)**
**Answer:** B. \(82^{\circ}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
In dilation, the shape is resized but retains its angles, so the measures of the angles remain unchanged regardless of the scale factor. Therefore, since triangle DEF is a dilation of triangle ABC, the largest angle in triangle DEF will also measure \( 82^{\circ} \). Imagining real-world situations, this type of geometric transformation appears in architecture and design. When engineers or architects create scaled models of buildings, they use dilation to ensure that the proportions and angles of the structures remain consistent, allowing for accurate representations in a smaller or larger form without altering the original design's angle measures.
