Question

explsin mid point theorum​

Answer 1

Answer:

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

Answer 2

Answer:

Step-by-step explanation:

Statement- The line segments joining the mid-points of any two sides are parallel to the third side and half of it.

Given- In triangle ABC, D and E are the mid-points of AB and AC respectively.

AD=DE and AE=EC

To prove- (i) DE is parallel to BC

(ii) DE=1/2BC

Construction- Produce DE up to F such that CF is parallel to AB

Proof-

(i) In triangle ADE and triangle FCE,

AE=CE (given)

Angle EAD=Angle ECF (alternate interior angles)

Angle AED=Angle FEC (vertically opposite angles)

By ASA congruence rule,

Triangle ADE is congruent to Triangle FEC

DE=EF

AD=CF

AD=DB

DB=CF

DB is parallel to CF

Hence, BCDF is a parallelogram.

(ii) DF=BC

DE+EF=BC

DE+DE=BC

2*DE=BC

DE=1/2BC

Hence, proved//