ABCD is a quadrilateral in which AD = BC and DAB = CBA (see Fig.) . Prove that (i) ΔABD ΔBAC (ii) BD = AC (iii) ABD = BAC

Solution

Given

AD = BC and ∠ DAB = ∠ CBA

To Prove

(i) ΔABD ΔBAC

(ii) BD = AC

(iii) ABD = BAC.

Proof

AD = BC, 

And ∠ DAB = ∠ CBA. 

On onsidering two triangles ΔABD and ΔBAC. 

AD = BC { As given }………………………………………….. (i) 

∠ DAB = ∠ CBA { As given also}……………………….. (ii) 

AB {Common side of both the triangle)…………. (iii) 

From the above three equation, two triangles ABD and BAC satisfies the SAS congruency criterion

So, ΔABD ≅ ΔBAC

(ii) 

BD and AC will be equal as they are corresponding parts of congruent triangles(CPCT). 

So BD = AC

(iii) Similarly,

∠ABD and ∠BAC will be equal as they are corresponding parts of congruent triangles(CPCT). 

So,

 ∠ABD = ∠BAC. 

Was this answer helpful?

  
   

0 (0)

Upvote (0)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class

Ask
Question