Question

In the given figure, D and E are the mid-points of
the sides AB and AC respectively. If BC = 6.6 cm,
B = 62°, compute (i) DE (ii) angle ADE.
E​

Answer 1

Answer:

It is given that,

D and E are the midpoint of sides AB and AC

BC=5.6 cm and ∠B=72

o

To find: DE

In △ABC,

D and E are the mid point of the sides AB and AC

⇒DE∥BC and DE=

2

1

BC[ Using mid point theorem ]

∴DE= 1/2 ×5.6=2.8 cm

Step-by-step explanation:

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Answer 2

Answer:

Here we join DE . and from converse of mid-point theorem , we get

DE  | | BC  , So

In Δ∆ ABC and Δ∆ ADE , we get

We take AB as transversal lines , So

∠∠ ABC  =  ∠∠ ADE                                      ( Corresponding angles )

So,

∠∠ ADE  =  62°°                                            ( Ans )

And

∠∠ ACB  =  ∠∠ AED                                      ( Corresponding angles )

So,

Δ∆ ABC ~~ Δ∆ ADE                                   ( by AA rule )

So,

ad/de = ab/bc

ad/dc = 2ad/6.6

1/de = 2/6.6

de = 6.6/2

therefore

DE=3.3 cm

Step-by-step explanation:

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