Triangle Inequalities Quiz

Consider the triangles shown. If mAngleUTV < mAngleUTS < mAngleSTR, which statement is true?

A: VU < US < SR by the hinge theorem.

Based on the given angle measures, which triangle has side length measures that could be correct?

D: (Fourth picture) A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.

In the diagram, MQ = QP = PO = ON. If NP is greater than MP, which must be true?

D: Angle O is larger than angle Q.

In the triangles, XY = MP and YZ = PN. If mP = 85°, which is a possible measure for Y?

C: mAngleY = 100°

Triangle XYZ is shown, where n ≥ 5. Which statements are true regarding the sides and angles of the triangle? Select three options.

B: Angle X is the largest angle. C: Angle Z is greater than angle Y. E: Line segment X Z is the shortest side.

In the triangles, QR = DE and SR = FE. Which statement about the sides must be true?

B: DF < QS

In the triangles, Line segment A C is-congruent-to line segment F E and Line segment B C is-congruent-to line segment D E. Which statement correctly compares Line segment A B and Line segment F D?

B: Line segment A B is longer than Line segment F D.

Consider the triangle. Triangle A B C is shown. Side A B has a length of 22, side B C has a length of 16, and side C A has a length of 12. Which shows the order of the angles from smallest to largest?

B: angle B, angle A, angle C

Gene starts from home and travels 3 miles north to the shopping mall. From the shopping mall, he travels 2 miles west to the library. Then, from the library, he travels about 3.6 miles to return home. The entire trip forms a triangle. The largest angle formed during his trip is _______.

B: at the mall

Consider the two triangles. If RT is greater than BA, which statement is true?

C: By the converse of the hinge theorem, mS > mC.

Consider the triangle. A triangle has 3 60 degree angles. Which statement is true about the lengths of the sides?

C: The three sides have the same length.

Choose the word that correctly completes the statement. Since angle B is the largest angle, Line segment A C is the ________ side.

C: longest

The side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3. Which is correct regarding the angles of the triangle?

C: mAngleC > mAngleA > mAngleB