Question

9. 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) triangleDCE = triangleLBE
(ii) AB = BL.
(iii) AL = 2DC​

Answer 1

Answer:

Given, ABCD is a parallelogram. E is mid point of BC.

Now, In △CED and △BEL

∠CED=∠BEL(Vertically opposite angles)

EC=BE (Given, E is mid point of BC)

∠DCE=∠EBL (Alternate angles)

Thus, △CED≅△BEL (SAS rule)

Hence, CD=BL (By cpct)

Since, CD=AB (ABCD is a parallelogram)

Thus, CD=BL=AB

Now, AL=AB+BL

AL=AB+AB

AL=2AB=2CD

Step-by-step explanation:

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