Question

unit #2 - lesson #2 exit ticket: below, ∠mnp is the image of ∠mvp after a 180° rotation about point c. the measure of ∠mvp is 41°. answer the following questions. (a) what is the measure of ∠mnp? explain. (b) name two things that are true about segments (overline{pn}) and (overline{pn}).

Explanation:

Step1: Recall rotation property

A 180 - degree rotation about a point changes the orientation of a figure. But the measure of an angle remains the same after a 180 - degree rotation.

Step2: Apply to the given angle

Since ∠M'N'P' is the image of ∠MNP after a 180 - degree rotation about a point, m∠M'N'P'=m∠MNP. Given m∠MNP = 41°, so m∠M'N'P'=41°.

Step3: Recall segment properties in rotation

In a 180 - degree rotation, the lengths of corresponding segments are equal. So, for segments $\overline{PN}$ and $\overline{P'N'}$, the following two facts are true: 1. The lengths of $\overline{PN}$ and $\overline{P'N'}$ are equal, i.e., $PN = P'N'$. 2. $\overline{PN}$ and $\overline{P'N'}$ are symmetric with respect to the center of rotation.

Answer:

(a) 41°
(b) 1. The lengths of $\overline{PN}$ and $\overline{P'N'}$ are equal. 2. $\overline{PN}$ and $\overline{P'N'}$ are symmetric with respect to the center of rotation.