91Ó°ÊÓ

Write a proof. Given \(\overline{\mathrm{JL}} \cong \overline{\mathrm{LN}}, \overline{\mathrm{KM}}\) is a midsegment of \(\triangle \mathrm{JLN}\) . Prove Quadrilateral JKMN is an isosceles trapezoid.

WRITING A FORMUL. AVrite a formula to nd the number of sides \(n\) in a regular polygon given that the measure of one exterior angle is \(x^{\circ}\) .

REASONINGIn Exercises \(37-40,\) i nd the number of sides for the regular polygon described. Each interior angle has a measure of \(156^{\circ} .\)

In Exercises \(37-42,\) the diagonall of rhombus \(\mathrm{ABCD}\) intersect at E. Given that \(\mathrm{m} \angle \mathrm{BAC}\) \(53^{\circ}, \mathrm{DE}\) \(8,\) and \(\mathrm{EC}\) 6 Find the indicated measure. $$ \mathrm{m} \angle \mathrm{DAC} $$

In Exercises \(37-42,\) the diagonall of rhombus \(\mathrm{ABCD}\) intersect at E. Given that \(\mathrm{m} \angle \mathrm{BAC}\) \(53^{\circ}, \mathrm{DE}\) \(8,\) and \(\mathrm{EC}\) 6 Find the indicated measure. $$ \mathrm{m} \angle \mathrm{AED} $$

Determine whether the points \(\mathrm{A}(4,5)\) \(\mathrm{B}(-3,3), \mathrm{C}(-6,-13),\) and \(\mathrm{D}(6,-2)\) are the vertices of a kite. Explain your reasoning,

REASONINGIn Exercises \(37-40,\) i nd the number of sides for the regular polygon described. Each interior angle has a measure of \(165^{\circ}\)

REASONINGIn Exercises \(37-40,\) i nd the number of sides for the regular polygon described. Each exterior angle has a measure of \(9^{\circ} .\)

In Exercises \(37-42,\) the diagonall of rhombus \(\mathrm{ABCD}\) intersect at E. Given that \(\mathrm{m} \angle \mathrm{BAC}\) \(53^{\circ}, \mathrm{DE}\) \(8,\) and \(\mathrm{EC}\) 6 Find the indicated measure. $$ \mathrm{m} \angle \mathrm{ADC} $$

PROVING A THEOREM Prove the Parallelogram Opposite Angles Converse (Theorem 7.8). (Hint: Let x ° represent m?A and m?C. Let y° represent m?B and m?D. Write and simplify an equation involving x and y. Given \(\angle A \cong \angle C, \angle B \cong \angle D\) Prove \(A B C D\) is a parallelogram.