Question

From the statement select the related given statement.

In a triangle a segment joining the midpoints of two sides is one-half the length of the third side.
A.) Plane R is parallel to plane S; Plane T cuts planes R and S.
B.) △ABC with ∠1 = ∠2.
C.) Point B is between points A and C
D.) Line l; point P not on l.
E.) △ABC with midpoints M and N.

Answer 1

MN = 1/2AB

Explanation:

Answer 2

The given statement is

In a triangle a segment joining the midpoints of two sides is one-half the length of the third side.

By, considering a Δ ABC and having mid points M and N

Angle A is common.

`(AM)/(AB) =(AN)/(AC)`

Δ A MN is similar to ΔABC.⇒[S AS]

As we know by CPCT if two triangles are similar their sides are proportional.

`(AM)/(AB) =(AN)/(AC)=(MN)/(BC)=(1)/(2)` [M and N are mid points of AB and AC]

Out of all five options Option (E) △ABC with midpoints M and N is correct which satisfies the above statement.