91Ó°ÊÓ

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

$\mathbf{m}\mathbf{∠}\mathbf{1}\mathbf{+}\mathbf{m}\mathbf{∠}\mathbf{2}\mathbf{=}\mathbf{m}\mathbf{∠}\mathbf{CDB}$

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

If $∠Kâ‰\dots ∠L$and $∠Lâ‰\dots ∠M$, then $∠Kâ‰\dots ∠M$.

If you head due east from Lily Bay Mountain (${90}^{∘}$ east of magnetic north), will you pass Bluff Mountain on your right or on your left?

Write something you can conclude from the given information.

Given:$AB=CD$

In the diagram, $\stackrel{↔}{AB}âŠ\yen \stackrel{↔}{CD}$and $\stackrel{↔}{EF}âŠ\yen \stackrel{↔}{GH}$. Name eight right angles.

Cut the Mobius band lengthwise down the middle. (Start at a point midway between the edges and cut around the band.) What is the result? Cut the band a second time down the middle. Write a sentence or two describing what happens.

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.

$\mathit{m}\mathbf{∠}\mathbf{5}\mathbf{=}\mathbf{31}$;$\mathbf{m}\mathbf{∠}\mathbf{7}\mathbf{=}\mathbf{31}$

$\mathit{m}\mathbf{∠}\mathbf{1}\mathbf{=}\mathbf{3}\mathit{x}\mathbf{-}\mathbf{5}$and $\mathit{m}\mathbf{∠}\mathbf{2}\mathbf{=}\mathit{x}\mathbf{+}\mathbf{25}$.

a.role="math" localid="1646463936005" $\mathit{x}\mathbf{=}\underset{\mathbf{¯}}{\mathbf{?}}$

b. $\mathit{m}\mathbf{∠}\mathbf{1}\mathbf{=}\underset{\mathbf{¯}}{\mathbf{?}}$(numerical value)

Complete. You may find that drawing a diagram will help you.

If $\stackrel{→}{BX}$is the bisector of $∠ABC$, then ___?___ role="math" $â‰\dots$___?___.

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

Write the converse of the conditional.