91Ó°ÊÓ

Supply reasons to justify the steps:

Use the conditional: If $m∠1=120$, then ∠1 is obtuse.

Write a definition of a straight angle as a biconditional.

Solve each system of equations by the substitution method.

$$\begin{gathered} 3x+2y=71 \\ y=4+2x \end{gathered}$$

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

If $\stackrel{↔}{AC}âŠ\yen \stackrel{→}{BE}$, then $∠ABE$is a right angle.

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.

$\stackrel{↔}{XZ}$bisects $∠WXY$.

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

Make a Mobius band. Let the band be 3 cm wide. Make a lengthwise cut, staying 1 cm form the right-hand edge. Describe the result.

Sailors use this method of finding their position when they are navigating near shore, sighting on lighthouses, smokestacks, and other landmarks shown on their charts. They call the small triangle formed by the three sighting lines a "cocked hat," and usually mark their position at the corner closest to the nearest hazard. Why is this a sensible rule?

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

If $a+7=b$and $b=4$, then $a+7=4$.

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

If D is the midpoint of $\stackrel{↔}{AB}$, then $AD=\frac{1}{2}AB$.