Triangles and Their Side Lengths

A B C (12, 15, x) The value of x must be greater than

3

If triangle DEF has a 90° angle at vertex E, which statements are true? Check all that apply.

The angle at vertex D is acute. Triangle DEF is a right triangle.

Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

b. AC + CB < AB

DE EF DF Which inequality explains why these three segments cannot be used to construct a triangle?

b. ED + EF < DF

Iliana claims that she can construct a triangle from a 12-inch rod, a 36-inch rod, and a 39.4-inch rod. Which statement explains whether she is correct?

c. Iliana will be able to construct a triangle because the sum of any two sides is greater than the third side.

In triangle XYZ, m<Z > m<X + m<Y. Which must be true about △XYZ?

d. m<X + m<Y < 90°

(Fiona's schools has three hallways that make up three sides) What are the possible lengths of the third hallway that she did not walk through?

d. between 30 yards and 150 yards

Triangle QRS has the angle measures shown. m<Q = (1x)° m<R = (3x)° m<S = (6x)° The measure of the obtuse angle equals

108

E D F Which statements about the diagram are true? Check all that apply.

DE + EF > DF 5 < DF < 13 △DEF is a scalene triangle.

Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be

a. less than 90°

Steven is cutting an 11ft piece of lumber into three pieces to build a triangular garden. Which diagram shows a way in which he can cut the wood to create three pieces that can form a triangle?

d. 3ft | 4ft | 4ft

Triangle QRS is a right triangle with the right angle of vertex R. The sum of m<Q and m<S must be

c. equal to 90°

Which are the possible side lengths of a triangle?

b. 4 cm, 8 cm, 10 cm