Question

in fig. 10.36 , point E is the mid-point of AC and BD both and BD =/ AC, then . 1. IS ∆CDB = ∆DBA? 2. IS ∆ CDB= ∆CAB?. 3. IS DC|| AB?. 4. IS DC= AB?.​

Answer 1

Answer:

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Answer 2

Answer:

hola there given: 

ABC is a triangle , D and E are the 

mid-points of the sides BC and AC respectively.

TPT: DE=1/2 AB

proof:

since D and E are the mid-points of the sides BC and AC respectively.

therefore CD=1/2 BC and EC=1/2 AC.

now in the triangle CED and triangle CAB,

∠ECD=∠ACB

and the ratio of the sides containing the angle is same. i.e.

\frac{cd}{ab} = \frac{1}{2} \: and \: \frac{ec}{ac} = \frac{1}{2}abcd=21andacec=21 

therefore the triangle CED and CAB are similar triangle.

hence the ratio of their corresponding sides will be equal.

hence 

\frac{de}{ab} = \frac{1}{2}abde=21 

i.e. DE=1/2 AB