91Ó°ÊÓ

For the following figure, given the two congruent angles$∠3â‰\dots ∠4$. Name two segments that must be congruent.

Prove the converse of the statement in Exercise 5: If both pairs of opposite sides of a quadrilateral are congruent, then they are also parallel.

Given:$\stackrel{¯}{SK}â‰\dots \stackrel{¯}{NR};\stackrel{¯}{SN}â‰\dots \stackrel{¯}{KR}$

Prove:$\stackrel{¯}{SK}âˆ\yen \stackrel{¯}{NR};\stackrel{¯}{SN}âˆ\yen \stackrel{¯}{KR}$

Write proofs in two-column form.

Given:$∠1â‰\dots ∠2;∠3â‰\dots ∠4$

Prove:$\mathrm{Δ}ADBâ‰\dots \mathrm{Δ}CBD$

Describe your plan for proving the following.

Given: $M$is midpoint of $\stackrel{¯}{AB}$; plane $XâŠ\yen \stackrel{¯}{AB}$at $M$

What can you deduce about$\stackrel{¯}{AP}$ and$\stackrel{¯}{BP}$

Complete.

Refer to $\mathrm{Δ}ABC$and name each of the following.

a. a median of$\mathrm{Δ}ABC$

b. an altitude of$\mathrm{Δ}ABC$

c. a bisector of an angle of $\mathrm{Δ}ABC$

For the following figure, can the triangle be proved congruent? If so, what postulate can be used?

In $△ABC$,$AB=7$ and $BC=7$. Write the theorem that allows you to conclude that $B$is on the perpendicular bisector of $\stackrel{¯}{\mathit{A}\mathit{C}}$.

For the following figure, find the value of $x$.

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to $\mathrm{Δ}ABC$. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.

Cut out any large triangle. Fold the two sides of one angle of the triangle together to form the angle bisector. Use the same method to form the bisectors of the other two angles. What do you notice?