91Ó°ÊÓ

Given: \(2 x-7=\frac{1}{3} x-2\) Prove: \(x=3\) Proof: \begin{array}{l|l}\hline \text { Statements } & \text { Reasons } \\\\\hline \text { a. } \underline{?} & \text { a. Given } \\\\\text { b. } \underline{?} & \text { b. Multiplication Property } \\\\\text { c. } 6 x-21=x-6 & \text { c. } \\\\\text { d. } \underline{?} & \text { d. Subtraction Property } \\\\\text { e. } 5 x=15 & \text { e. } \\\\\text { f. } \underline{?} & \text { f. Division Property }\end{array}

Write a proof for each theorem. Transitive Property of Angle Congruence

Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. \(p: \sqrt{-64}=8\) q: A triangle has three sides. \(r: 0<0\) s: An obtuse angle measures greater than 90 and less than 180 . $$p \wedge s$$

Write each statement in if-then form. Get a free water bottle with a one-year gym membership.

Make a conjecture based on the given information. Draw a figure to illustrate your conjecture. \(B D\) is an angle bisector of \(\angle A B C\).

Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. \(p: \sqrt{-64}=8\) q: A triangle has three sides. \(r: 0<0\) s: An obtuse angle measures greater than 90 and less than 180 . $$\sim q \wedge r$$

State the property that justifies each statement. $$\text { If } x(y+z)=a, \text { then } x y+x z=a$$

Write each statement in if-then form. Math teachers love to solve problems.

Use the Law of Syllogism to determine whether a valid conclusion can be reached from each set of statements. If a valid conclusion is possible, write it. If not, write no conclusion. If two lines intersect to form a right angle, then they are perpendicular. Lines \(\ell\) and \(m\) are perpendicular.

State the property that justifies each statement. If \(n-17=39,\) then \(n=56\)