Find values for r and t such that the inequality r < s < t best describes s, the length of the third sides of a triangle for which the lengths of the other two sides are given. 12 and 31.

Find values for r and t such that the inequality r < s < t best describes s, the length of the third sides of a triangle for which the lengths of the other two sides are given. 2 and 4

ΔABC is scalene and C̅M̅ is a median to side A̅B̅. a. Tell whether each given statement is True or False. b. If the statement is true, state the definition, postulate, or theorem that justifies your answer. m∠ACM > m∠BCM

If a, b, and c are positive real numbers such that a>b and b>c, tell whether the relationship is always true, sometimes true, or never true. If the statement is always true, state the postulate illustrated. If the statement is sometimes true, give one example for which it is true and one for which it is false: If the statement is never true, give one example for which it is false

$$c-a>c-b$$

a. Draw a diagram to illustrate the hypothesis and tell whether each conclusion is true or false. b. State a postulate or a definition that justifies your answer. If SR > KR and SR = TR, then TR > KR.

Name the smallest angle of $\triangle A B C$, using the given information.

If $\angle E F H$ is an exterior angle of $\triangle F G H, \ m\angle E F H=125, \ m\angle G=65, \ m\angle H=60$, list the sides of $\triangle F G H$ in order starting with the shortest.

In the below case use an inequality postulate to prove the conclusion.

If a=b, then 180-a>90-b.

ΔABC is scalene and C̅M̅ is a median to side A̅B̅. a. Tell whether each given statement is True or False. b. If the statement is true, state the definition, postulate, or theorem that justifies your answer. BA > MB

Points P and Q lie on the perpendicular bisector of $\overline{A B}$. Which of the following statements must be true?

(1) $\overline{A B}$ is the perpendicular bisector of $\overline{P Q}$. (2) $P A=P B$ and $Q A=Q B$. (3) $P A=Q A$ and $P B=Q B$. (4) P is the midpoint of $\overline{A B}$ or Q is the midpoint of $\overline{A B}$.

Given: $\triangle A B C \cong \triangle C D A$, $A D>D C$

Prove: (a). $\ m\angle A C D>\ m\angle C A D$ (b). $\overline{A C}$ does not bisect $\angle A$.

Tell in each case whether the given lengths can be the measures of the sides of a triangle. 5, 8, 11

a. Draw a diagram to illustrate the hypothesis and tell whether each conclusion is true or false. b. State a postulate or a definition that justifies your answer. If m∠1 > m∠2 and m∠2 > m∠3, then m∠1 > m∠3.

If a, b, and care positive real numbers such that a > b and b > c, tell whether each relationship is always true, sometimes true, or never true. If the statement is always true, state the postulate illustrated. If the statement is sometimes true, give one example for which it is true and one for which it is false. If the statement is never true, give one example for which it is false. a + c > b + c

Name the smallest angle of $\triangle A B C$, using the given information.

If $\angle A B D$ is an exterior angle of $\triangle B C D, \ m\angle A B D=118, \ m\angle D=60$, and $\ m\angle C=58$, list the sides of $\triangle B C D$ in order starting with the longest.