Question

plzz answer this PLZ plzz plzzz plzzz and explain step by step​

Answer 1

Answer:

ΔABC ≅ ΔEDC

Step-by-step explanation:

First we will find the equal angles...

∠GBA lies on the line sengment GBC. So,

the measure of ∠ABC = 180 - ∠GBA (linear pair of angles)

Similarly, as we know that ∠GBA = ∠FDE (given in question)

So, ∠EDC = 180 - ∠FDE (linear pair of angles)

We can also say that, ∠EDC = 180 - ∠GBA (because ∠FDE = ∠GBA)

∴ We can conclude that since ∠FDE = ∠GBA, So, ∠ABC = ∠EDC

Now, taking AB ║ DE, and taking line GF as a transversal, we can say that,

∠BCA = ∠DCE (vertically opposite angles)

∴ The next pair of equal angles is ∠BCA = ∠DCE

So now we have, ∠ABC = ∠EDC and ∠BCA = ∠DCE...

In the question it is  also given that CB = CD

So now we have two pairss of equal angles and one pair of equal sides to verify the ASA Criterion.

∴ ∠ABC = ∠EDC, ∠BCA = ∠DCE and CB = CD

So, ΔABC ≅ ΔEDC by ASA.

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