In an Isosceles Triangle ABC, point D lies on segment BC. Angle B is 4

Question

In an Isosceles Triangle ABC, point D lies on segment BC. Angle B is 40 degrees. What is the value of angle DAB?

(1) AD is angular bisector of angle A.
(2) AB x CD = AC x BD

viktorija · Answer

Can anybody explain why the answer is E?

raj44 · Answer

The answer is E because the question stem doesn't specify which 2 angles are equal, angle A or angle C could both be equal to 40. Also, the 2 statements mean the same- AD as angle bisector itself means ab x bd = ac x dc

anupamadw · Answer

Unable to understand how ab x bd = ac x dc means AD is angle bisector?

ab ac
--- = ----
bd dc

means ABD and ACD are simliar triangles , not same triangles.
Sides are in proportion, does it mean angles are same?

Kindly clarify.

KarishmaB · Answer

It's the angle bisector theorem. Check Wiki here: https://en.wikipedia.org/wiki/Angle_bisector_theorem

ssriva2 · Answer

Bunuel ,
I have one query here.
Does the angle bisector extends 90 degree angle at base?

Bunuel · Answer

Sorry, I don't understand what you mean...

ssriva2 · Answer

I hope its clear now.i have attached figure for same

Bunuel · Answer

Only for for an isosceles triangle (or for an equilateral), the angle bisector to base coincides with the height.

EgmatQuantExpert · Answer

Hi ssriva2 , You can also understand this property in the following manner. Refer the diagram below: https://e-gmat.com/blogs/wp-content/uploads/2015/05/GC-ISC1-e1432649725681.jpg In the diagram, ABC is an isosceles triangle with sides AB = AC. As angles opposite the equal sides are equal we have ∠B = ∠C = x . Also AD is the angle bisector of ∠A, therefore ∠BAD = ∠CAD = \frac{y}{2} . We can also see from the above figure that ∠BDA = ∠CDA = z (as ∠BDA = ∠CDA = 180 - x - \frac{y}{2} ) We also know that in triangle ABC, 2x + y = 180 . Similarly in triangle ABD we can write z + x + \frac{y}{2} = 180 i.e. 2z + 2x + y = 360 . Since 2x + y = 180 , we have 2z + 180 = 360 i.e. z = 90 . However please note that the only the angle bisector of the non-equal angle of an isosceles triangle will be perpendicular to the opposite base i.e. the non-equal side. Also AD bisects base BC i.e. BD = DC. These properties will not apply to the equal angles and the equal sides . In case of an equilateral triangle, we know that x = 60 and \frac{y}{2} = 30 , hence z = 90 . In an equilateral triangle since all angles and sides are equal, these properties would apply to any of the angles and sides . Hope it's clear

Regards Harsh

Madhavi1990 · Answer

So based on this itself why is it E? why not D?

In an Isosceles Triangle ABC, point D lies on segment BC. Angle B is 4

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GMAT Data Sufficiency (DS) Questions

In an Isosceles Triangle ABC, point D lies on segment BC. Angle B is 4

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