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.

Use the Chapter $14$ Geometer's Sketchpad activity Orthocenter on our Web site to investigate a wide range of acute, obtuse, and right triangles. Do your conclusions for parts $\mathrm{a}, \mathrm{b}$, and $c$ still hold?

True or false? Justify your reasoning.

c. All equilateral triangles are congruent.

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.

c. Where does the orthocenter of an obtuse triangle ?

True or false? Justify your reasoning.

c. All isosceles right triangles are congruent.

True or false? Justify your reasoning.

b. All isosceles triangles are similar.

True or false? Justify your reasoning.

b. If two triangles are congruent, they are similar.

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.

b. Where does the orthocenter of a right triangle lie ?

The \triangle LMN and \triangle GHI are shown.

Name two other sets of corresponding information that would allow you to apply the SAS congruence property.

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

b. A hexagon

Construct the angle bisector for each of the following angles.

The \triangle ABC and \triangle WXY are shown.

Name two other sets of corresponding information that would allow you to apply the SAS congruence property.

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

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

a. A square

True or false? Justify your reasoning.

a. All isosceles triangles are congruent.