Question

In the adjoining figure, given angle is of a° , construct angle ABC and angle DBC such that a) angle ABC=a° b) angle DBC= 1/2 a° ​

Answer 1

Answer:

34

Step-by-step explanation:

1. In quadrilateral ACBD, AC = AD and AB bisects ∠A )see figure). Show that ΔABC ≌ ΔABD. What can you say about BC and BD?

Ans. In quadrilateral ABCD we have

AC = AD

and AB being the bisector of ∠A.

Now, in ΔABC and ΔABD,

AC = AD

[Given]

AB = AB

[Common]

∠CAB = ∠DAB [∴ AB bisects ∠CAD]

∴ Using SAS criteria, we have

ΔABC ≌ ΔABD.

∴ Corresponding parts of congruent triangles (c.p.c.t) are equal.

∴ BC = BD.

2. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that

(i) ΔABD ≌ ΔBAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.