Questions: In the figure, MN is perpendicular to OP and MP = MQ. Complete the sentence. 1. Name the legs of isosceles triangle PMQ. 2. Name the base of isosceles triangle PMQ. 3. Name the hypotenuse of right triangle PNM. 4. Name the legs of right triangle PNM. 5. Name the acute angles of right triangle QNM.

In the figure, MN is perpendicular to OP and MP = MQ. Complete the sentence. 1. Name the legs of isosceles triangle PMQ. 2. Name the base of isosceles triangle PMQ. 3. Name the hypotenuse of right triangle PNM. 4. Name the legs of right triangle PNM. 5. Name the acute angles of right triangle QNM.
Transcript text: In the figure, $\overline{M N} \perp \overline{O P}$ and $\overline{M P}=\overline{M Q}$. Complete the sentence. 1. Name the legs of isosceles triangle $\triangle P M Q$. 2. Name the base of isosceles triangle $\triangle P M Q$. 3. Name the hypotenuse of right triangle $\triangle P N M$. 4. Name the legs of right triangle $\triangle P N M$. 5. Name the acute angles of right triangle $\triangle Q N M$.
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Solution

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Name the legs of isosceles triangle \( \triangle PMQ \).

Identify the isosceles triangle.

The isosceles triangle is \( \triangle PMQ \), where \(\overline{MP} = \overline{MQ}\).

Identify the legs.

The legs of an isosceles triangle are the two equal sides. In \( \triangle PMQ \), the legs are \(\overline{MP}\) and \(\overline{MQ}\).

\(\boxed{\overline{MP}, \overline{MQ}}\)

Name the base of isosceles triangle \( \triangle PMQ \).

Identify the isosceles triangle.

The isosceles triangle is \( \triangle PMQ \), where \(\overline{MP} = \overline{MQ}\).

Identify the base.

The base of an isosceles triangle is the side that is not equal to the other two. In \( \triangle PMQ \), the base is \(\overline{PQ}\).

\(\boxed{\overline{PQ}}\)

Name the hypotenuse of right triangle \( \triangle PNM \).

Identify the right triangle.

The right triangle is \(\triangle PNM \) since \(\overline{MN} \perp \overline{OP}\).

Identify the hypotenuse.

The hypotenuse of a right triangle is the side opposite the right angle. In \( \triangle PNM \), the hypotenuse is \(\overline{MP}\).

\(\boxed{\overline{MP}}\)

\(\overline{MP}, \overline{MQ}\) \(\overline{PQ}\) \(\overline{MP}\)

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