91Ó°ÊÓ

Complete.

$m∠FOB=\underset{¯}{?}$

Prove the following statement by filling in the blanks.

If A and B have coordinated a and b, with $b>a$, and the midpoint M of $\stackrel{¯}{AB}$ has coordinate x, then prove $x=\frac{a+b}{2}$.

Proof:

Write a plan for a proof.

Given: $∠\mathbf{3}$is a supplement of $∠1$;

$∠4$is a supplement of $∠2$.

Prove:$∠\mathbf{3}â‰\dots ∠\mathbf{4}$.

Find the value of $x$.

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

$∠1$and$∠3$ are complementary.

Classify each statement as true or false. If it is false, provide a counter example.

If$m∠A=45°$, then the complement of∠Ais one third of its supplement.

Copy everything shown and write a two column proof.

Given:$∠2â‰\dots ∠3$

Prove:$∠1â‰\dots ∠4$

In line 50, $P\left(n\right)$could instead be computed from the series

$1−\frac{1}{2}+\frac{1}{4}−\frac{1}{8}+\mathrm{...}+{\left(−\frac{1}{2}\right)}^{n−1}$

where each term of the series reflects the bee’s return half of the way from $P_{n−1}$to $P_{n−2}$. Replace line 50 with the line below and RUN the new program.

50 LET ­$P\left(N\right)=P\left(N−1\right)+\left(−1/2\right)↑\left(N−1\right)$

Check that both programs produce the same results. (Some slight variations will be expected, due to rounding off.)

Use the conditional: If $\stackrel{¯}{AB}$and $\stackrel{¯}{CD}$intersect, then $\stackrel{→}{AB}$and $\stackrel{→}{CD}$intersect.

Write the converse of the conditional. Is the converse true or false?

State the hypothesis and the conclusion of each conditional.

I can’t sleep if I’m not tired.