Q2 Quiz 1 - Proving Midline Theorem

The Midline Theorem states that the segment connecting the midpoints of two sides of a triangle is:

• Equal to the third side

• Half the length of the third side

• Twice the length of the third side

• Perpendicular to the third side

• One-third of the third side

Answer explanation

What is another name for the midline of a triangle?

• Base

• Midsegment

• Median

• Altitude

• Bisector

Answer explanation

A segment joining midpoints of two sides is commonly called a midsegment or midline.

• AB

• AC

• BC

• AD

• CD

Answer explanation

If D and E are midpoints of AB and AC, then DE is parallel to the side BC.

• 2

• 1

• 3

Answer explanation

Which method is commonly used to prove the Midline Theorem?

• Trigonometry

• Two-column proof using congruent triangles

• Pythagorean Theorem

• Law of Sines

• Law of Cosines

Answer explanation

The usual elementary proof constructs two triangles and uses congruence (often SAS) to show corresponding angles are equal. yielding parallelism and length relation.

Answer explanation

Which congruence postulate is often applied in proving midline Theorem?

• SSS

• SAS

• ASA

• HL

• CPCTC

Answer explanation

Many proofs use SAS to show two triangles are congruent (equal sides come from midpoint segments and a shared side/angle), then use CPCTC to conclude parallelism/length.

Answer explanation

• DL bisects ES

• DL is an altitude

Answer explanation

Always true for a midline : it is PARALLEL to the third line (by Midline Theorem).

Which of the following best describes the role of the Midline Theorem in geometry?

• It helps solve equations involving angles.

• It establishes relationships between triangles and parallel lines.

• It explains the Pythagorean Theorem.

• It proves the similarity of quadrilaterals.

• It supports coordinate proofs in triangles.

Answer explanation

The Midsegment (Midline) Theorem creates a clear link between midpoints, parallelism, and proportional lengths in triangles - a key structural relationship used widely in geometry.