Construct the bisector of $\angle R$ using a compass and straightedge.

The lines containing the altitudes of a triangle meet at a single point, called the orthocenter. The position of the orthocenter is determined by the measures of the angles. Construct the three altitudes for each of the following triangles. Then complete the statements in parts a-c.

a. Where does the orthocenter of an acute triangle lie ?

Describe how to construct the following regular $n$-gons.

a. A square

The \triangle ABC and \triangle WXY are shown.

To apply the SAS congruence property to prove $\triangle A B C \cong \triangle W X Y$, you could show that $\overline{A B} \cong$ ?, that $\angle B \cong$ ?, and that $\overline{B C} \cong ?$.

Construct the bisector of $\angle R$ using a compass and straightedge.

Construct the angle bisector for each of the following angles.

The \triangle LMN and \triangle GHI are shown.

Suppose $\angle G \cong \angle M$. Identify the rest of the information needed to prove $\triangle G H I \cong \triangle M L N$ using the SAS congruence property.

True or false? Justify your reasoning.

a. All isosceles triangles are congruent.

Trace \angle DEF. Then construct the bisector $\overrightarrow{E G}$ of $\angle D E F$.

Prove that the diagonals of a parallelogram bisect each other.

Construct a regular $12$-$\textit{gon}$ with a compass and straightedge.

Prove that if a trapezoid is isosceles, its opposite angles are supplementary.

Draw an angle and bisect it.

Describe three ways to calculate the height of a tree using similarity.