Question

In quadrilateral ABCD
AC=AD and AB bisects angle A. Show that triangle ABC is congruent to triangle ABD. What can you say about BC and BD?

Answer 1

Answer:

BC it congruent to BD (By congruent side of congruent traingles)

Explanation:

In triangle ABC and triangle ABD

Side AC = Side AD (Given) ......... 1

Angle BAC = Angle BAD ( AB bisects angle ABC) ..........2

Side AB = side AB ( Common side) .........3

Therefore from 1 ,2 and 3

Triangle ABC is congruent to Triangle ABD ...........( By SAS test)

Answer 2

Question :-

In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see figure). Show that ∆ABC ≅ ∆ABD. What can you say about BC and BD?

Answer :-

In quadrilateral ACBD, we have AC = AD and AB being the bisector of ∠A.

Now, In ∆ABC and ∆ABD,

AC = AD (Given)

∠ CAB = ∠ DAB ( AB bisects ∠ CAB)

and AB = AB (Common)

∴ ∆ ABC ≅ ∆ABD (By SAS congruence axiom)

∴ BC = BD (By CPCT)

Plz mrk as brainliest ❤