What does the Mid-Point Theorem state?

The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and is equal to half of it.

In triangle ABC, if D and E are the midpoints of sides AB and AC respectively, what is the relationship between DE and BC?

DE is parallel to BC and DE = 1/2 BC.

True or False: The converse of the Mid-Point Theorem states that a line drawn through the midpoint of one side of a triangle, parallel to another side, bisects the third side.

True.

Riddle: I connect midpoints and create parallels, bisecting lines in geometric tales. What am I?

Mid-Point Theorem

Fill in the blank: A straight line drawn through the midpoint of one side of a triangle, parallel to another side, ______ the third side.

Bisects

In quadrilateral ABCD, if P, Q, R, and S are midpoints of sides AB, BC, CD, and DA respectively, what shape is formed?

A parallelogram.

Which theorem states that if a transversal makes equal intercepts on three or more parallel lines, any other transversal will also make equal intercepts?

Equal Intercept Theorem.

True or False: In a right-angled triangle, the median to the hypotenuse is equal to half the length of the hypotenuse.

False. The median to the hypotenuse is equal to half the length of the hypotenuse.

Fill in the blank: If DE is parallel to BC and D is the midpoint of AB, then DE ______ AC.

Bisects

What is the formula for the length of segment EF joining midpoints of non-parallel sides of a trapezium?

EF = 1/2 (AB + DC).

Riddle: I’m a line that cuts through midpoints, creating two equal lengths when aligned. What am I?

A bisector.

In triangle ABC, if AD and BE are medians meeting at point G, what is significant about point G?

Point G is the centroid of triangle ABC.

True or False: The Mid-Point Theorem can only be applied to triangles.

False. It can also be applied to quadrilaterals.

Fill in the blank: In parallelogram ABCD, if P is the midpoint of AB and Q is the midpoint of CD, then ______ is true.

PB = DQ

What does the Equal Intercept Theorem imply about intercepts made by transversals on parallel lines?

It implies that equal intercepts will remain equal on any other transversal cutting them.

Riddle: Known for my parallel lines, I help bisect without divide. What theorem am I?

Converse of Mid-Point Theorem

In a parallelogram, if EF is parallel to AB and is the mid-segment, what can be said about EF's length?

EF is equal to 1/2 the sum of the lengths of AB and DC.

True or False: In triangle ABC, if D is the midpoint of AC, then BD is always perpendicular to AC.

False. BD is not necessarily perpendicular to AC.

Fill in the blank: In trapezium ABCD, if E is the midpoint of AD and a line through E is drawn parallel to AB, then it intersects BC at point ______.

F

What does the Mid-Point Theorem state about the line segment joining the midpoints of two sides of a triangle?

The line segment is parallel to the third side and is equal to half of it.