Question

Answer it with Explanation.​

Answer 1

Answer:

In ΔABD and ΔBAC

AD = BC                     [Given]

∠DAB = ∠CBA           [Given]

AB = AB                      [Common side]        

∴ By SAS congruent criteria,

ΔABD ≅ ΔBAC

∴ BD = AC [Corresponding parts of congruent triangle {CPCT}]

HOPE THIS HELPS YOU......

PLZ MARK AS BRAINLEST......

Answer 2

Answer- The above question is from the chapter 'Triangles'.

Triangle: A Triangle is a three-sided polygon with three vertices and three angles.

There are 5 criterion of congruency:

1. SSS (Side-Side-Side Criterion)

2. SAS (Side-Angle-Side Criterion)

3. ASA (Angle-Side-Angle Criterion)

4. RHS (Right-Hypotenuse-Side Criterion)

5. AAS (Angle-Angle-Side Criterion)

Given question: ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA.

Prove that (i) ΔABD ≅ ΔBAC (ii) BD = AC

(Figure has been attached in the question.)

Solution:

Given: ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA.

To prove: (i) ΔABD ≅ ΔBAC

(ii) BD = AC

Proof: In  ΔABD and ΔBAC.

S→ AD = BC (given)

A→ ∠DAB = ∠CBA (given)

S→ AB = BA (common)

∴ ΔABD ≅ ΔBAC  (by SAS Congruence Criterion)

(ii) BD = AC [by CPCT (Corresponding parts of congruent triangles)]