converse of mid point theorem
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864
converse of mid-point theorem: it states that in a triangle line drawn from the mid-point of the one side of triangle, parallel to the other side intersect the third side at its mid-point.
6given: ABC is a triangle. and D is the mid-point of AB.
from D a line DE is drawn parallel to BC, intersect AC at E.
TPT: E is the mid-point of AC.
construction: extend DE. from C draw a line CF parallel to BA, which intersect produced DE at F.
proof:
since BD is parallel to CF (by the construction)
and DF is parallel to BC (given)
BDFC is a parallelogram.
BD= CF [opposite sides of the parallelogram are equal]
AD= BD [D is the mid-point of AB]
AD= CF......(1)
in the triangle AED and CEF,
∠AED=∠CEF
∠ADE=∠EFC
AD=CF [from (1)]
therefore by the AAS congruency triangles are congruent.
thus AE = EC
i.e. E is the mid-point of AC.
hope this helps you.
cheers!!
Plz mark it as brainliest...
6given: ABC is a triangle. and D is the mid-point of AB.
from D a line DE is drawn parallel to BC, intersect AC at E.
TPT: E is the mid-point of AC.
construction: extend DE. from C draw a line CF parallel to BA, which intersect produced DE at F.
proof:
since BD is parallel to CF (by the construction)
and DF is parallel to BC (given)
BDFC is a parallelogram.
BD= CF [opposite sides of the parallelogram are equal]
AD= BD [D is the mid-point of AB]
AD= CF......(1)
in the triangle AED and CEF,
∠AED=∠CEF
∠ADE=∠EFC
AD=CF [from (1)]
therefore by the AAS congruency triangles are congruent.
thus AE = EC
i.e. E is the mid-point of AC.
hope this helps you.
cheers!!
Plz mark it as brainliest...
Answered by
426
Hi friend..
See the attached files..
I hope it will help you mate
✌️
See the attached files..
I hope it will help you mate
✌️
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