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

a. A square

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.

For which of the following values of $n$ can a regular $n$-gon be constructed with a compass and straightedge?

d. $4369$

Decide whether $\triangle A B C \cong \triangle D E F$ under the following conditions. Which of the properties in Exercise $2$ justify the congruences? If the triangles are not congruent, sketch a figure to show why not.

d. $\angle B \cong \angle E, \overline{B C} \cong \overline{E F}, \overline{A B} \cong \overline{D E}$

Decide whether $\triangle A B C \sim \triangle D E F$ under the following conditions. Which of the properties in Exercise 2 justify the similarity? If the triangles are not similar, sketch a figure to show why not.

$$\angle B \equiv \angle E, \angle C \equiv \angle F$$

Decide whether $\triangle A B C \cong \triangle D E F$ under the following conditions. Which of the properties in Exercise $2$ justify the congruences? If the triangles are not congruent, sketch a figure to show why not.

c. $\angle A \cong \angle D, \angle B \cong \angle E, \overline{A B} \cong \overline{D E}$

For which of the following values of $n$ can a regular $n$-gon be constructed with a compass and straightedge?

c. $144$