Question

triangle def is a dilation of triangle abc with scale factor 2. in triangle abc, the largest angle measures 82°. what does the largest angle measure in triangle def?
a 41°
b 82°
c 98°
d 164°
2 draw 2 polygons that are similar but could be mistaken for not being similar. explain why they are similar.

Explanation:

Question 1

Step1: Recall the property of similar triangles

When a triangle is dilated, the resulting triangle is similar to the original triangle.

Step2: Use the property of similar triangles' angles

Similar triangles have congruent corresponding angles. Since triangle \(DEF\) is a dilation of triangle \(ABC\), \(\triangle ABC\sim\triangle DEF\). The largest angle of \(\triangle ABC\) is \(82^{\circ}\), so the largest angle of \(\triangle DEF\) is also \(82^{\circ}\)

• Drawing: Draw a square with side - length \(2\) units and another square with side - length \(3\) units.
• Explanation: For two polygons to be similar, their corresponding angles must be equal and their corresponding side lengths must be in proportion. In the case of squares, all angles are \(90^{\circ}\). Let the side lengths of the first square be \(a = 2\) and of the second square be \(b=3\). The ratio of their side lengths is \(\frac{a}{b}=\frac{2}{3}\). For any two squares, the ratio of side lengths \(k\) (scale factor) is constant for all sides, and all angles are \(90^{\circ}\). They might be mistaken for not being similar because of the difference in size, but by the definition of similar polygons (equal - angle measures and proportional side lengths), they are similar.

Answer:

B. \(82^{\circ}\)

Question 2