Relationship in Triangles

Name the shortest side of Triangle ABC.

• AB

• BC

• AC

Answer explanation

The shortest side is always across from the smallest angle.

Two sides of a triangle are 7 and 12 inches. What is the range of the possible side length of the third side?

• 5 < x < 19

• 4 < x < 8.5

• 8< x < 11

• 4 < x < 20

Answer explanation

The range of the possible side length of the third side is 5 < x < 19. This choice satisfies the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Two sides of a triangle are 8 and 8 inches. What is the range of the possible side length of the third side?

• 5 < x < 19

• 8 < x < 16

• 1 < x < 15

• 0 < x < 16

Answer explanation

The range of the possible side length of the third side is 0 < x < 16. This is the correct choice because it satisfies the triangle inequality theorem.

When you draw the perpendicular bisectors of a triangle it creates the point of concurrency called the _____________.

• Centroid

• Incenter

• Circumcenter

• Orthocenter

Answer explanation

The point of concurrency created by drawing the perpendicular bisectors of a triangle is called the circumcenter. It is the center of the circle that passes through all three vertices of the triangle.

The centroid is the point of concurrency of the 3 ____ of a triangle. 

• Medians

• Midsegments

• Perpendicular Bisectors

• Angle Bisectos

Answer explanation

The centroid is the point where the medians of a triangle intersect.

QR is a midsegment of triangle WUV. What is the length of segment QR?

• 4

• 8

• 16

• 32

Which of the following terms best describes Angle d?

• Remote interior angle

• Corresponding angle

• Exterior angle

• Interior angle

What segment is parallel to EF?

• Segment PM

• Segment MN

• Segment NP

• Segment FG

What is the measure of angle Y?

• 60

• 40

• 140

• 100

What is the measure of angle X?

• 60

• 40

• 140

• 100