91Ó°ÊÓ

Some information about the diagram is given. Tell whether the other statements can be deduced from what is given. (Write Yes or No).

Given: Point B lies interior of $∠AOC$.

a. $m∠1=m∠2$

b. $m∠AOC=m∠1+m∠2$

c. $m∠AOC>m∠1$

d. $m∠AOC>m∠2$

e. $m∠1>m∠2$

f. $m∠AOC=90$

Suppose someone plans to write an indirect proof of each conditional. Write a correct first sentence of the indirect proof.

If $\stackrel{¯}{DF}\cancel{â‰\dots }\stackrel{¯}{RT}$, then$\stackrel{¯}{DE}\cancel{â‰\dots }\stackrel{¯}{RS}$

Complete the following statement with the word always, sometimes, or never.

Two lines parallel to the same plane _____ intersect.

Suppose someone plans to write an indirect proof of each conditional. Write a correct first sentence of the indirect proof.

If $\stackrel{¯}{DF}\cancel{â‰\dots }\stackrel{¯}{RT}$, then $\stackrel{¯}{DE}\cancel{â‰\dots }\stackrel{¯}{RS}$

For the following conditional statement, classify the statement as true or false.

If $4b>20$, then $b>5$.

Complete the proof $m∠2>m∠4$if $m∠2>m∠1$is given.

Write the contrapositive of the converse of the inverse of the conditional: if r, then s.

Given: Points $R,S,T,$and $W;\stackrel{↔}{RS}$and $\stackrel{→}{TW}$are skew.

Prove: $\stackrel{↔}{RT}$and $\stackrel{↔}{SW}$are skew.

Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.

If $m∠A+m∠B≠180°$then $m∠D+m∠C≠180°$.

Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.

If $n^2$is not a multiple of 3, then n is not a multiple of 3.