91Ó°ÊÓ

a. Draw a large scalene triangle $\mathbf{ABC}$. Carefully draw the bisector of $∠\mathbf{A}$, the altitude from $\mathbf{A}$, and the median from $\mathbf{A}$. These three should all be different.

b. Draw a large isosceles triangle $\mathbf{ABC}$with vertex angle $\mathbf{A}$. Carefully draw the bisector of $∠\mathbf{A}$, the altitude from $\mathbf{A}$, and the median from $\mathbf{A}$. Are these three different?

Describe your plan for proving the following.

1. Given:$\stackrel{\mathbf{¯}}{\mathbf{P}\mathbf{R}}$ bisects$\mathbf{∠}\mathit{Q}\mathit{P}\mathit{S}\mathbf{;}\stackrel{\mathbf{¯}}{\mathbf{P}\mathbf{Q}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{P}\mathbf{S}}$ Prove:$\mathbf{∠}\mathit{Q}\mathbf{â‰\dots }\mathbf{∠}\mathit{S}$

For the following figure, state which congruence method can be used to prove the triangle congruent. If no method applies, say none.

Suppose you wish to prove $\mathbf{Δ´¡¹ó·¡}\mathbf{â‰\dots }\mathbf{Δ\mu þ¹ó\P Ù}$. If you have already proved $\mathrm{Δ}\mathbf{ABE}â‰\dots \mathrm{Δ}\mathbf{BAD}$, what corresponding parts from this second pair of congruent triangles would you use to prove the first pair of triangles congruent?

In Exercises 1-6 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.

Prove:$\stackrel{¯}{\mathrm{NE}}â‰\dots \stackrel{¯}{\mathrm{OS}}$

Key steps of proof:

a.$\mathrm{Δ}\mathbf{RNX}â‰\dots \mathrm{Δ}\mathbf{LOY}$

b.$∠\mathbf{X}â‰\dots ∠\mathbf{Y}$

c.$\mathrm{Δ}\mathbf{NEX}â‰\dots \mathrm{Δ}\mathbf{OSY}$

d.$\stackrel{¯}{\mathrm{NE}}â‰\dots \stackrel{¯}{\mathrm{OS}}$

If$\mathrm{Δ}AOD$ is isosceles, with $\stackrel{¯}{OA}â‰\dots \stackrel{¯}{OD}$. Then$∠\_\_â‰\dots ∠\_\_$?

In Exercises 1–3 you are given a diagram that is marked with given information. Give the reason for each key step of the proof.

a.$\mathrm{Δ}\mathbf{ABC}â‰\dots \mathrm{Δ}\mathbf{DEF}$

b.$∠\mathbf{C}â‰\dots ∠\mathbf{F}$

c.$\mathrm{Δ}\mathbf{ACS}â‰\dots \mathrm{Δ}\mathbf{DFT}$

d.$\stackrel{¯}{\mathrm{AS}}â‰\dots \stackrel{¯}{\mathrm{DT}}$

Suppose that $\mathrm{Δ}BIGâ‰\dots \mathrm{Δ}CAT$, then complete the following statement.

$∠Gâ‰\dots \_\_$

In the following figure, the two-triangle shown are congruent. Then complete the following statement.

$\mathrm{Δ}STWâ‰\dots \mathrm{Δ}\_\_\_$

Complete.

If $â–³BADâ‰\dots â–³TOP$, then role="math" localid="1649245739017" $\stackrel{¯}{DB}â‰\dots \underset{\_}{?}$and role="math" localid="1649245766553" $â–³PTOâ‰\dots \underset{\_}{?}$.