91Ó°ÊÓ

$ABCDEFGHIJ$is a regular decagon. If sides $\stackrel{¯}{AB}$and $\stackrel{¯}{CD}$ extended to meet at K, find the measure of $∠K$.

Copy what is shown for Theorem 3-7 on page 84. Then write a proof in two column form.

Exercises 23-29 refer to the diagram in step 2 of exercise 22.

Name five lines that appear to be parallel to$\stackrel{¯}{\mathrm{AG}}$.

Given:$\stackrel{¯}{\mathit{A}\mathit{B}}âŠ\yen \stackrel{¯}{\mathit{B}\mathit{C}};\stackrel{¯}{\mathit{B}\mathit{D}}âŠ\yen \stackrel{¯}{\mathit{A}\mathit{C}}$

1. If $m∠C=22$, find $m∠ABD$.
2. If $m∠C=23$, find_{$m∠ABD$}.
3. Explain why $m∠ABD$ always equal$m∠C$.
   
   

Draw several diagrams to help you decide whether each statement is true or false. If it is false, show a counterexample. It is true, draw and label a diagram you could use in a proof. List, in terms of the diagram, what is given and what is to be proved. Do not write a proof.

If the diagonals of a quadrilateral are congruent and also perpendicular, then the quadrilateral is a regular quadrilateral.

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If two lines do not intersect, then they are parallel.

Draw a four-sided figure $ABCD$with $\stackrel{¯}{AB}âˆ\yen \stackrel{¯}{DC}$and$\stackrel{¯}{AD}âˆ\yen \stackrel{¯}{BC}$

1. Prove that$∠Aâ‰\dots ∠C$
2. Is $∠Bâ‰\dots ∠D$?

Plot each point on graph paper.

$O(0,0)$.

$\stackrel{¯}{BC}$is one side of a regular n-gon. The sides next to $\stackrel{¯}{BC}$ are extended to meet at W. Find the measure of $∠W$ in terms of n.

Given: $\stackrel{¯}{BE}$bisects $∠DBA;∠3â‰\dots ∠1$

Prove: $\stackrel{¯}{CD}||\stackrel{¯}{BE}$