91Ó°ÊÓ

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

Given:$m∠A+m∠B=180;m∠C=m∠B$

What property of equality justifies the statement $m∠A+m∠C=180$?

Write the name or statement of the definition, postulate, or theorem that justifies the statement about the diagram.

If$\stackrel{↔}{DF}$ bisects $∠CDB$, then $∠1â‰\dots ∠2$.

Write something you can conclude from the given information.

Given: $BE=EF$; E is the midpoint of $\stackrel{¯}{FC}$.

Name the definition or state the theorem that justifies the statement about the diagram.

If $\stackrel{→}{BE}âŠ\yen \stackrel{↔}{AC}$, then $∠ABD$and $∠DBE$are complementary.

a. In each exercise use the information given to conclude that two angles are congruent.

b. Name or state the definition or theorem that justifies your conclusion.

∠4 is supplementary to ∠6; ∠2 is supplementary to ∠7;$∠6â‰\dots ∠7$

Name or state the postulate, property, definition, or theorem that justifies the statement.

If $a+7=4$, then $a=−3$.

$\stackrel{→}{OB}$is the bisector of $∠AOC$and $\stackrel{→}{OC}$is the bisector of $∠BOD$. $m∠AOC=60$. Find$m∠COD$

Solve each system of equations by the substitution method.

$\begin{array}{c}4x-5y=92\\ x=7y\end{array}$

In the diagram, $\stackrel{→}{BE}âŠ\yen \stackrel{↔}{AC}$and $\stackrel{→}{BD}âŠ\yen \stackrel{→}{BF}$. Find the measures of the following angles.

Take two long narrow strips of paper. Fasten them together so they are perpendicular and form sign. Twist one strip so it is a Mobius band and fasten its ends together. Don’t twist the other strip at all, just fasten its ends. Cut the Mobius band down the middle lengthwise. Then cut the other band down the middle. Describe the final result.