Exploring the Triangle Midsegment Theorem Proof

What does the Triangle Mid-Segment Theorem state?

• The segment joining the midpoints of any two sides of a triangle is parallel to the third side and half its length.

• The segment joining the midpoints of any two sides of a triangle is twice the length of the third side.

• The segment joining the midpoints of any two sides of a triangle is perpendicular to the third side.

• The segment joining the midpoints of any two sides of a triangle is equal to the third side.

What is the first step in proving a geometry theorem?

• Memorizing the theorem.

• Sketching the situation.

• Writing down the theorem statement.

• Finding the area of the triangle.

Which two concepts are essential for proving the Triangle Mid-Segment Theorem?

• Circle Theorems and Tangent Properties

• Area of Triangles and Law of Cosines

• Triangle Similarity and Converse of the Corresponding Angles Theorem

• Pythagorean Theorem and Sine Rule

What is the length of segment AD if D is the midpoint of AC and AC is 2X?

• 3X

• X/2

• 2X

• X

Which postulate is used to prove that triangle AED is similar to triangle ABC?

• Angle-Angle (AA)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

What is the ratio of the lengths of AD to AC if D is the midpoint of AC?

• 1:2

• 1:1

• 2:1

• 1:3

If DE is half the length of CB, what is the length of CB if DE is Z?

• Z

• 3Z

• 2Z

• Z/2

What must be true for two line segments to be considered parallel?

• They must be perpendicular to a common line.

• The lines containing the segments must be parallel.

• They must form a right angle with a transversal.

• They must be equal in length.

Which angles are used to prove that DE is parallel to CB?

• Alternate interior angles

• Corresponding angles

• Vertical angles

• Supplementary angles

What theorem is used to conclude that DE is parallel to CB?

• Midpoint Theorem

• Converse of the Corresponding Angles Theorem

• Pythagorean Theorem

• Angle Bisector Theorem