Triangle Midsegment Theorem: Introduction and Basic Practice

Which statement best defines a midsegment of a triangle?

• A line passing through the triangle’s centroid

• A segment connecting two vertices of the triangle

• A segment perpendicular to the third side at its midpoint

• A segment connecting the midpoints of two sides

According to the Triangle Midsegment Theorem, a midsegment in a triangle is ______ to the third side and ______ its length.

• perpendicular; twice

• parallel; equal to

• perpendicular; equal to

• parallel; half

In triangle ABC, D and E are midpoints of AB and AC. If BC = 18, what is DE?

• 9

• 12

• 18

• 6

In triangle ABC, DE is the midsegment with endpoints on AB and AC. If DE = 7, which statement is true?

• BC = 14 and DE ∥ BC

• BC = 7 and DE ⟂ BC

• AB = 14 and DE ∥ AB

• AC = 7 and DE ∥ AC

Given triangle PQR with L, M, N as midpoints of PQ, QR, and PR, which segments must be parallel?

• LM ∥ PQ, MN ∥ PR, LN ∥ PR

• LM ∥ PR, MN ∥ PQ, LN ∥ QR

• LM ∥ PR, MN ∥ QR, LN ∥ PQ

• LM ∥ QR, MN ∥ PR, LN ∥ PQ

Triangle sides AB and AC have midpoints D and E. If AD = 5 and AE = 7, which is the most accurate statement about DE?

• DE is parallel to BC

• DE is perpendicular to BC

• DE is equal to AB

• DE bisects BC

In triangle CDE, points F and G are midpoints of CE and CD. If CG = 12 and CE = 30, what is FG?

• 15

• 9

• 12

• 7.5

In triangle ABC, DE is a midsegment with D on AB and E on AC. If AB = 18 cm and AC = 26 cm, which statement is always true?

• DE bisects BC and equals 26 cm

• DE is parallel to BC and equals 13 cm

• DE is parallel to BC and equals 22 cm

• DE is perpendicular to BC and equals 9 cm

In triangle PQR, M and N are midpoints of PQ and PR. If QR = 30, what is MN?

• MN = 30

• MN = 15

• MN = 12

• MN = 20

In triangle XYZ, segment LM is a midsegment with L on XY and M on XZ. If LM = 7 and YZ = 3x − 1, find x.

• x = 6

• x = 8

• x = 5

• x = 7