91Ó°ÊÓ

Draw a diagram for the following:

a.$M$ is the point between$A$and$B$.

b.$M$ is the midpoint of$\stackrel{¯}{AB}$.

Use the information given in each exercise to name the method $\mathbf{(}\mathit{S}\mathit{A}\mathit{S}\mathbf{,}\mathbf{}\mathit{A}\mathit{A}\mathit{S}\mathbf{,}\mathbf{}\mathit{S}\mathit{S}\mathit{S}\mathbf{,}\mathbf{}\mathit{A}\mathit{S}\mathit{A}\mathbf{,}\mathbf{}\mathbf{or}\mathbf{}\mathit{H}\mathit{L}\mathbf{)}$you could use to prove $\mathit{Δ}\mathbf{\text{ }}\mathit{A}\mathit{O}\mathit{B}\mathbf{â‰\dots }\mathit{Δ}\mathit{A}\mathit{O}\mathit{C}$.You need not write the proofs.

Given $\stackrel{\mathbf{¯}}{\mathbf{A}\mathbf{O}}\mathbf{âŠ\yen }\mathbf{\text{±è±ô²¹²Ô±ð }}\mathit{M}\mathbf{;}\mathbf{}\stackrel{\mathbf{¯}}{\mathbf{B}\mathbf{O}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{C}\mathbf{O}}$

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

Given:$\stackrel{\mathbf{¯}}{\mathbf{M}\mathbf{B}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{N}\mathbf{C}}\mathbf{;}\stackrel{\mathbf{¯}}{\mathbf{B}\mathbf{N}}\mathbf{âŠ\yen }\stackrel{\mathbf{¯}}{\mathbf{A}\mathbf{C}}\mathbf{;}\stackrel{\mathbf{¯}}{\mathbf{C}\mathbf{M}}\mathbf{âŠ\yen }\stackrel{\mathbf{¯}}{\mathbf{A}\mathbf{B}}$

Prove:$\stackrel{\mathbf{¯}}{\mathbf{C}\mathbf{M}}\mathbf{â‰\dots }\stackrel{\mathbf{¯}}{\mathbf{B}\mathbf{N}}$

Complete.

$△\mathbf{CAP}$and$△\mathbf{TAP}$ are equilateral and coplanar.$\stackrel{¯}{\mathrm{AP}}$ is a common side of the two triangles.$\mathbf{m}∠\mathbf{CAT}=\underset{\_}{?}$ (numerical answer).

Can you deduce from the given information that $â–³\mathbf{RXY}â‰\dots â–³\mathbf{SXY}$? If so, what postulate can you use?

Given:$\stackrel{¯}{\mathrm{RX}}â‰\dots \stackrel{¯}{\mathrm{SX}}$; $\stackrel{¯}{\mathrm{RY}}â‰\dots \stackrel{¯}{\mathrm{SY}}$

Complete.

If $\mathit{R}$is on the perpendicular bisector of $\stackrel{\mathbf{¯}}{\mathit{S}\mathit{T}}$, then $\mathit{R}$is equidistant from $\underset{\mathbf{¯}}{\mathbf{?}}$and $\underset{\mathbf{¯}}{\mathbf{?}}$. Thus $\underset{\mathbf{¯}}{\mathbf{?}}\mathbf{=}\underset{\mathbf{¯}}{\mathbf{?}}$.

$\stackrel{→}{\mathrm{UV}}$bisects $∠\mathbf{WUX}$. Write the theorem that justifies the statement that$\mathbf{V}$ is equidistant from$\stackrel{→}{\mathrm{UW}}$ and $\stackrel{→}{\mathrm{UX}}$.

Draw a large scalene right triangle. Then draw the perpendicular bisectors of its three sides and tell whether they appear to meet in a point. If so, where is this point?

Describe your plan for proving the following.

Given: $\stackrel{¯}{CD}âŠ\yen \stackrel{¯}{AB};D$is midpoint of $\stackrel{¯}{AB}$Prove: $\stackrel{¯}{CA}â‰\dots \stackrel{¯}{CB}$