Question

for the following problems, \\( \triangle mit \cong \triangle her \\)

1. \\( m \angle m = \square ^ { \circ } \\)
2. \\( m \angle t = \square ^ { \circ } \\)
3. \\( mt = \square \mathrm { cm } \\)
4. \\( \overline { i m } \cong \square \\)

Explanation:

Step1: Use triangle angle - sum property

In \(\triangle HER\), by the angle - sum property of a triangle (\(m\angle E + m\angle H+m\angle R=180^{\circ}\)), we can find \(m\angle R\).
\(m\angle R=180-(32 + 79)=69^{\circ}\)
Since \(\triangle MIT\cong\triangle HER\), corresponding angles are equal.

Step2: Find \(m\angle M\)

\(\angle M\) and \(\angle H\) are corresponding angles. So \(m\angle M = m\angle H\)
\(m\angle M = 79^{\circ}\)

Step3: Find \(m\angle T\)

\(\angle T\) and \(\angle E\) are corresponding angles. So \(m\angle T=m\angle E\)
\(m\angle T = 32^{\circ}\)

Step4: Find \(MT\)

\(MT\) and \(HE\) are corresponding sides. So \(MT = HE\)
\(MT=7\mathrm{cm}\)

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

\(\overline{IM}\) and \(\overline{RH}\) are corresponding sides. So \(\overline{IM}\cong\overline{RH}\)

Answer:

1. \(79\)
2. \(32\)
3. \(7\)
4. \(\overline{RH}\)