91Ó°ÊÓ

Write a two-column or flowchart proof. [ Note: For the remainder of the book, the key will only show a two-column proof. This is done for efficiency.] (Angle can't copy) \(\begin{aligned} \text {Given:} & \overrightarrow{A C} \text { bisects } \angle B A D \\ & \overrightarrow{C A} \text { bisects } \angle B C D \end{aligned}\) Prove: \(\angle B \cong \angle D\)

Draw a segment about 2 inches long and a second segment 5 inches long. Construct an isosceles triangle with the base as the 2 -inch segment and each side as the 5 -inch segment.

Construct a right triangle with legs about 2 inches and 3 inches in length, respectively.

Write a two-column or flowchart proof. [ Note: For the remainder of the book, the key will only show a two-column proof. This is done for efficiency.] (Angle can't copy) Given: \(\overrightarrow{D B}\) bisects \(\angle A D C\) \(\overline{A D} \cong \overline{C D}\) Prove: \(\overline{D B} \perp \overline{A C}\)

Construct a right isosceles triangle with legs that are about 2 inches in length.

Every triangle has three altitudes, angle bisectors, and medians. Describe the differences among these line segments.

Draw a scalene acute triangle and construct its three altitudes. Label the orthocenter.

Given: \(\mathrm{Cis}\) the midpoint of \(\overline{A E}\) and of \(\overline{B D}, \overline{A B} \perp \overline{B D},\) and \(\overline{D E} \perp \overline{B D}\) Prove: \(\triangle A B C \cong \triangle E D C\)

Draw a scalene obtuse triangle and construct its three altitudes. Label the orthocenter.

Draw a scalene obtuse triangle and construct its three medians. Label the centroid.