Triangle Inequalities

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

d. 8 | 16.1 | 14

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

d. Angle O is larger than angle Q.

Triangle XYZ is shown, where n>_5. Which statements are true regarding the sides and angles of the triangle? Check all that apply?

Angle X is the largest angle. Angle Z is greater than angle Y. XZ is the shortest side

Lee is creating a garden with the dimensions shown. He creates paths through the garden along AB, XY, and ZY. Which correctly compares the lengths of the paths?

a. The path along XY is longer than the path along ZY, and the path along ZY is longer than the path along AB

Consider the triangles shown. U S V T R If m<UTV < m<UTS < m<STR, which statement is true?

a. VU < US < SR by the hinge theorem.

T U V | 5 units, 8 units, 11 units Which statement is true regarding triangle TUV?

b. Angle V is the smallest angle

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

b. DF < QS

Consider the triangle. A C B | 12, 22, 16 Which shows the order of the angles from smallest to largest?

b. angle B, angle A, angle C

Consider the two triangles. B A C | R S T If RT is greater than BA, which statement is true?

c. By the converse of the hinge theorem, m<S > M<C.

Consider the triangle. 60°, 60°, 60° Which statement is true about the lengths of the sides?

c. The three sides have the same length.

The side lengths of triangle A B C are written in terms of the variable p, where p>_ 3. Which is correct regarding the angles of the triangle?

c. m<C > m<A > m<B

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. m<C > m<A > m<B

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

c. m<Y = 100°

Complete the statement. A: 60°, B: 75°, C: 45° Since angle B is the largest angle, AC is the ____________ side.

longest

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 made during his trip is at

the mall