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Byju's Answer

Standard X

Mathematics

Criteria for Similarity of Triangles

From the give...

Question

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid point of BC.

Hence, $Δ D C E ≅ Δ L B E$
State true or false.

True

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False

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Solution

The correct option is A True
In $△$ s $D C E$ and $L B E,$
$∠ D E C = ∠ B E L$ (Vertically opposite angles)

$∠ E D C = ∠ E L B$ (Alternate angles for parallel lines CD and AL)

$E C = E B$ (Given)
Hence, $△ E D C ≅ E L B$ (AAS postulate)

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Similar questions

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid point of BC.

Hence, AL = 2DC

If the above statement is true then mention answer as 1, else mention 0 if false

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid point of BC.

Prove that :

(i) $Δ$ DCE $≅ Δ$ LBE

(ii) AB = BL.

(iii) AL = 2DC

From the given diagram, in which $A B C D$ is a parallelogram, $A B L$ is a line segment and E is mid point of BC. Hence, $AB = BL.$

If the above statement is true then mention answer as 1, else mention 0 if false

Q. State true or false:

In parallelogram

A B C D

E

and

F

are mid-points of the sides

A B

and

C D

respectively. The line segments

A F

and

B F

meet the line segments

E D

and

E C

at points

G

and

H

respectively, then

G E H F

is a parallelogram.

State true or false:

E

is the mid-point of side

A B

and

F

is the midpoint of side

D C

of parallelogram

A B C D

, then

A E F D

is a parallelogram.

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From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid point of BC.Hence,ΔDCE≅ΔLBEState true or false.

The correct option is A TrueIn △s DCE and LBE,∠DEC=∠BEL (Vertically opposite angles)∠EDC=∠ELB (Alternate angles for parallel lines CD and AL)EC=EB (Given)Hence, △EDC≅ELB (AAS postulate)

From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid point of BC.

Hence, $Δ D C E ≅ Δ L B E$
State true or false.

The correct option is A True
In $△$ s $D C E$ and $L B E,$
$∠ D E C = ∠ B E L$ (Vertically opposite angles)

$∠ E D C = ∠ E L B$ (Alternate angles for parallel lines CD and AL)

$E C = E B$ (Given)
Hence, $△ E D C ≅ E L B$ (AAS postulate)