Please find below the solution to the asked query:
From given information we form our diagram , As :

Here , BC | | DE and D is mid point of AB , From converse of mid point theorem we get that
E is also a mid point of AC , So
AE = EC , ( Given EC = 5 cm )
Then ,
AE = 5 cm ( Ans )
And
ADDE = ABBC⇒AD6 = 2 ADBC⇒16 = 2BC⇒BC = 12 cm ( Ans )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Answers
Given: In triangle ABC, D and E are midpoints of AB and AC respectively.
To Prove:
DE || BC
DE = 1/2 BC
Construction: Draw CR || BA to meet DE produced at R. (Refer the above figure)
∠EAD = ∠ECR. (Pair of alternate angles) ———- (1)
AE = EC. (∵ E is the mid-point of side AC) ———- (2)
∠AEP = ∠CQR (Vertically opposite angles) ———- (3)
Thus, ΔADE ≅ ΔCRE (ASA Congruence rule)
DE = 1/2 DR ———- (4)
But, AD= BD. (∵ D is the mid-point of the side AB)
Also. BD || CR. (by construction)
In quadrilateral BCRD, BD = CR and BD || CR
Therefore, quadrilateral BCRD is a parallelogram.
BC || DR or, BC || DE
Also, DR = BC (∵ BCRD is a parallelogram)
⇒ 1/2 DR = 1/2 BC
The Converse of MidPoint Theorem
The line drawn through the mid–point of one side of a triangle and parallel to another side bisects the third side.
See the attachment is given...✌️❤️
