91Ó°ÊÓ

Prove the Triangle Angle-Bisector Theorem.

The lengths of the sides of \(\triangle A B C\) are \(B C=12 . C A=13\) and \(A B=14 .\) If \(M\) is the midpoint of \(\overline{C A}\). and \(P\) is the point where \(\overline{C A}\) is cut by the bisector of \(\angle B\). find \(M P\).

Find the measure of each angle. The ratio of the measures of two supplementary angles is 11: 4

Find the measure of each angle. The measures of the angles of a triangle are in the ratio 3: 4: 5

Find the measure of each angle. The measures of the acute angles of a right triangle are in the ratio 5: 7 .

Prove that there cannot be a triangle in which the trisectors of an angle also trisect the opposite side.

Draw two equiangular hexagons that are clearly not similar.

Can there exist a \(\triangle R O S\) in which the trisectors of \(\angle O\) intersect \(\overline{R S}\) at \(D\) and \(E\), with \(R D=1 . D E=2 .\) and \(E S=4 ?\) Explain.

The measures of the consecutive angles of a quadrilateral are in the ratio \(5: 7: 11: 13 .\) Find the measure of each angle. draw a quadrilateral that satisfies the requirements, and explain why two sides must be parallel.

A basketball player has made 24 points out of 30 free throws. She hopes to make all her next free throws until her free-throw percentage is 85 or better. How many consecutive free throws will she have to make?