91Ó°ÊÓ

M is the midpoint of $\stackrel{¯}{AB}$, Q is the midpoint of $\stackrel{¯}{AM}$, and T is the midpoint of $\stackrel{¯}{QM}$. If the coordinates of A and B are a and b, find the coordinates of Q and T in terms of a and b.

Given: $∠2â‰\dots ∠3$.

a. What can you deduce?

b. Explain how you would prove your conclusion.

Find the value of x.

Copy everything shown and write a two-column proof.

Given: $\stackrel{¯}{AC}âŠ\yen \stackrel{¯}{BC}$;∠3 is complementary to∠1.

Prove:$∠3â‰\dots ∠2$

In the diagram, $\stackrel{→}{\mathrm{OB}}$bisects $∠\mathbf{AOC}$and $\stackrel{\mathit{↔}}{EC}\mathit{âŠ\yen }\stackrel{\mathit{↔}}{OD}$.

Find the value of x.

$m∠5=2x$, $m∠3=x$.

Can you conclude from the information given for the exercise that $\stackrel{→}{XY}âŠ\yen \stackrel{→}{XZ}$?

$m∠1=m∠4$

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If $∠Aâ‰\dots ∠B$, then $m∠A=m∠B$.

Point T is the midpoint of $\stackrel{¯}{RS}$, W is the midpoint of $\stackrel{¯}{RT}$, and Z is the midpoint of $\stackrel{\mathit{¯}}{\mathit{W}\mathit{S}}$. If the length of $\stackrel{\mathit{¯}}{\mathit{T}\mathit{Z}}$ is x, find the following lengths in term of x. (Hint: Sketch a diagram and let $y=WT$.)

a. RW

b. ZS

c. RS

d. WZ

Copy everything shown and write a two-column proof.

Given: $m∠1=m∠2$; $m∠3=m∠4$.

Prove:$\stackrel{→}{YS}âŠ\yen \stackrel{↔}{XZ}$

Can you conclude from the information given for the exercise that $\stackrel{→}{XY}âŠ\yen \stackrel{→}{XZ}$?

$∠1$and role="math" localid="1646422063897" $∠3$ are congruent and complementary.