Relationship in Triangles

What is the length of segment ZY ?

• cannot be determined

• 1.35

• 5.4

• 2.7

Put the sides of the triangle in order from smallest to largest.

• TS, RT, RS

• TS, RS, RT

• RT, TS, RS

• RS, RT, TS

Put the angles in order from smallest to largest.

• X, Y, Z

• Z, X, Y

• Y, X, Z

• Y, Z, X

The figure is an example of a(n) ...

• angle bisector

• perpendicular bisector

• median

• midsegment

Answer explanation

The figure represents an angle bisector, which divides an angle into two congruent angles.

What is point J called?

• centroid

• incenter

• circumcenter

• orthocenter

Answer explanation

Point J is called the centroid, which is the point of intersection of the medians of a triangle. It is the balance point of the triangle, where the medians divide each other in a 2:1 ratio.

The centroid cuts each median into two segments.  The shorter segment is ___________ the length of the entire segment.

• one third

• two thirds

• three fourths

• one half

Answer explanation

The shorter segment is one third the length of the entire segment.

CF, BE, and AD are the medians of the triangle. If BF =10, find AF.

• 20

• 10

• 5

• Not Enough Information

Answer explanation

The median of a triangle divides the opposite side into two equal parts. Since BF = 10, AF must also be 10 to maintain the balance of the triangle.

If G is the centroid of triangle ABC and GF= 4. Find the length of GC.

• 4

• 8

• 12

• Not Enough Information

Answer explanation

The centroid of a triangle divides each median in a 2:1 ratio. Since GF is 4, GC is twice that length, which is 8. Therefore, the length of GC is 8.

H is the circumcenter. Find CD. If your answer is a decimal, round to the nearest tenth.

H is the circumcenter. Find HD. If your answer is a decimal, round to the nearest tenth.