Question

EXERCISE 7.1
1. In quadrilateral ACBD,
AC = AD and AB bisects ZA
(see Fig. 7.16). Show that A ABCEA ABD.
What can you say about BC and BD?
Fig. 7.16​

Answer 1

Answer:

∆Abc and ∆abd

Ac=Ad (given)

ab=ab common

angle bac= angle bad (ab bisect )

∆abc congruent ∆abd (by SAS rule)

bc= bd (by cpct)

Answer 2

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Given,

AC = AD and AB bisects ∠A

To prove,

ΔABC ≅ ΔABD

Proof,

In ΔABC and ΔABD,

AB = AB (Common)

AC = AD (Given)

∠CAB = ∠DAB (AB is bisector)

Therefore, ΔABC ≅ ΔABD by SAS congruence condition.

BC and BD are of equal length.