Question

use the figure to answer the following questions.

1. mr = 24; hr=
2. tr = 16; at=
3. mh = 58; mr=
4. r is the mid - point of and

Explanation:

Step1: Identify congruent segments

From the figure, we can see that $\overline{MR}\cong\overline{HR}$ and $\overline{TR}\cong\overline{AR}$ because of the equal - segment markings.

Step2: Solve for HR when MR = 24

Since $\overline{MR}\cong\overline{HR}$, if $MR = 24$, then $HR=24$.

Step3: Solve for AT when TR = 16

Since $\overline{TR}\cong\overline{AR}$, and $AT=AR + TR$, and $TR = 16$, $AR = 16$, so $AT=16 + 16=32$.

Step4: Solve for MR when MH = 58

Since $\overline{MR}\cong\overline{HR}$ and $MH=MR + HR$, and $MR = HR$, then $MR=\frac{MH}{2}$. Given $MH = 58$, so $MR = 29$.

Step5: Identify mid - point segments

From the equal - segment markings, $R$ is the mid - point of $\overline{MH}$ and $\overline{TA}$.

Answer:

1. 24
2. 32
3. 29
4. $\overline{MH}$, $\overline{TA}$