91Ó°ÊÓ

Write the hypothesis and the conclusion of each conditional. If \(3 x-7=32,\) then \(x=13\)

Two complementary angles are congruent. Find their measures.

Rewrite each pair of conditionals as a biconditional. If \(m \angle A O C=180,\) then \(\angle A O C\) is a straight angle. If \(\angle A O C\) is a straight angle, then \(m \angle A O C=180\).

Provide a counterexample to show that each statement is false. You may use words or a diagram. If a four-sided figure has four right angles, then it has four congruent sides.

Prove Theorem \(2-8:\) If two angles are complements of congruent angles, then the two angles are congruent. Note: You will need to draw your own diagram and state what is given and what you are to prove in terms of your diagram. (Hint: See the proof of Theorem 2-7 on page 61.)

Point \(T\) is the midpoint of \(\overline{R S} . W\) is the midpoint of \(\overline{R T},\) and \(Z\) is the midpoint of \(\overline{W S}\). If the length of \(\overline{T Z}\) is \(x\). find the following lengths in terms of \(x .\) (Hint: Sketch a diagram and let \(y=W T\).) a. \(R W\) b. \(Z S\) c. \(R S\) d. \(W Z\)

Use the given information to write an equation and solve the problem. Find the measure of an angle that is twice as large as its supplement.

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false. Write a definition of congruent angles as a biconditional.

Use the given information to write an equation and solve the problem. The measure of a supplement of an angle is 12 more than twice the measure of the angle. Find the measures of the angle and its supplement.

Use the given information to write an equation and solve the problem. A supplement of an angle is six times as large as a complement of the angle. Find the measures of the angle. its supplement, and its complement.