QuestionCTIICE
1. If two polygons are similar, must they also be congruent? Explain.
Decide whether the figures are similar. Explain your reasoning. 2.
In the diagram, TUVW $\sim A B C D$. 3.
4. List all pairs of congruent angles and write the statement of proportionality for the polygons.
5. Find the scale factor of $T U V W$ to $A B C D$.
6. Find the length of $\overline{T W}$.
7. Find the measure of $\angle T U V$. 8.3 Similar Polygons

Studdy Solution
Determine the measure of $\angle TUV$:
- Since TUVW $\sim$ ABCD, $\angle TUV = \angle ABC$. - $\angle ABC$ is given as 70°. - Therefore, $\angle TUV = 70°$.
The solutions to the problems are as follows:
1. Similar polygons are not necessarily congruent unless the scale factor is 1.
2. The rectangles in Problem 2 are not similar.
3. The quadrilaterals in Problem 3 are not similar.
4. Congruent angles: $\angle T = \angle A$, $\angle U = \angle B$, $\angle V = \angle C$, $\angle W = \angle D$. Proportionality: $\frac{TU}{AB} = \frac{UV}{BC} = \frac{VW}{CD} = \frac{WT}{DA}$.
5. Scale factor: $\frac{5}{3}$.
6. Length of $\overline{TW}$: 10.
7. Measure of $\angle TUV$: 70°.