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 ____. *

1: 3
1:1
2:1
1:2​

Answer 1

Answer:

1 : 1

Step-by-step explanation:

As E is the midpoint of AC, so AE = EC,

Thus their ratio is, AE : EC = 1 : 1

Answer 2

Answer:

1:1

Step-by-step explanation:

DE is parallel to BC

So, In triangles ABC , ADE

∠

DAE =

∠

ECF {Alternate angles}

∠

ADE =

∠

EFC {Alternate angles}

∠

BAC

=

∠

DAE

By A.A.A similarity ABC

≡

ADE

⇒

AD

DB

=

AE

EC

(

Basic

Proportionality

Theorem

)

Since

,

D

is

midpoint

of

AB

.

AD

=

DB

⇒

AD

DB

=

1

1

=

AE

EC

⇒

AE

EC

=

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

∠

DAE =

∠

ECF {Alternate angles}

∠

ADE =

∠

EFC {Alternate angles}

△

ADE ≡

△

CFE

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

AE: EC = 1: 1

In triangles ADE