Question

In ABC ,Given that DE//BC , D is the midpoint of AB and E is a midpoint of AC. The ratio AE : EC is ____.

• A. 1:2
• B. 2:1
• C. 1:1
• D. None of the above

Answer 1

The correct option is C

1:1

DE is parallel to BC

So, In triangles ABC , ADE

$\angle$DAE = $\angle$ECF {Alternate angles}

$\angle$ADE = $\angle$EFC {Alternate angles}

∠BAC = ∠DAE
By A.A.A similarity ABC≡ADE
⇒ADDB=AEEC ( Basic Proportionality Theorem )Since, D is midpoint of AB .AD=DB⇒ADDB=11=AEEC⇒AEEC=1
ALTERNATE SOLUTION

D is the midpoint of AB. A line segment DE is drawn which meets AC in E and is parallel to the opposite side BC.

BCFD is a parallelogram DF || BC and CF || BD

CF = BD {opposite sides of parallelogram are equal}

CF = DA {Since BD = DA given}

In $△$ ADE and $△$ CFE

AD = CF

$\angle$DAE = $\angle$ECF {Alternate angles}

$\angle$ADE = $\angle$EFC {Alternate angles}

$△$ ADE ≡ $△$ CFE

AE = EC {Corresponding parts of congruent triangles are equal}

AE: EC = 1: 1



In triangles ADE