for the following problems, ( riangle mitcong riangle her ) 13. ( mangle m=square^{circ} ) 14. ( mangle t=square^{circ} ) 15. ( mt=square cm ) 16. ( overline{im}congsquare )

Question

for the following problems, ( 	riangle mitcong	riangle her ) 13. ( mangle m=square^{circ} ) 14. ( mangle t=square^{circ} ) 15. ( mt=square cm ) 16. ( overline{im}congsquare )

Accepted Answer

# Explanation:
## Step1: Use the property of congruent triangles
Since $\triangle MIT\cong\triangle HER$, corresponding angles and sides are equal. That is $\angle M=\angle E$, $\angle T = \angle H$, $\angle I=\angle R$, $MT = EH$, $IM=RE$, $IT = HR$

## Step2: Find $m\angle M$
We know that $\angle E = 32^{\circ}$ (given in $\triangle HER$). Since $\angle M=\angle E$ (corresponding angles of congruent triangles $\triangle MIT\cong\triangle HER$), so $m\angle M = 32^{\circ}$

## Step3: Find $m\angle T$
We know that $\angle H=77^{\circ}$ (given in $\triangle HER$). Since $\angle T=\angle H$ (corresponding angles of congruent triangles $\triangle MIT\cong\triangle HER$), so $m\angle T = 77^{\circ}$

## Step4: Find $MT$
We know that $EH = 7\mathrm{cm}$ (given in $\triangle HER$). Since $MT = EH$ (corresponding sides of congruent triangles $\triangle MIT\cong\triangle HER$), so $MT=7\mathrm{cm}$

## Step5: Find $\overline{IM}$
We know that $\overline{RE}$ (in $\triangle HER$ $RE = 6\mathrm{cm}$). Since $\overline{IM}\cong\overline{RE}$ (corresponding sides of congruent triangles $\triangle MIT\cong\triangle HER$), so $\overline{IM}\cong\overline{RE}$

# Answer:
13. $32$
14. $77$
15. $7$
16. $\overline{RE}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of congruent triangles

Step2: Find \(m\angle M\)

Step3: Find \(m\angle T\)

Step4: Find \(MT\)

Step5: Find \(\overline{IM}\)

Answer: