BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Geometry

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 134
Joined: Sun Jul 25, 2010 5:22 am
Thanked: 1 times
Followed by:2 members

Geometry

by gmatusa2010 » Fri Sep 17, 2010 5:57 am
Picture: https://tinyurl.com/33lglbj


If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD

(1) AND (2) SUFFICIENT: Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD). We also know that angle BAD is a right angle, so side BD is the hypotenuse of right isosceles triangle BAD. If each leg of the triangle is 5, the hypotenuse (using the Pythagorean theorem) must be 5.

Can someone explain the bolded part?
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Fri Sep 17, 2010 6:37 am
This is more of a Geometry rule. So you will need to remember this.
in an ISOCELES triangle, the Perpendicular from the vertex bisects the non-equal side.
Opposite is also true.

Hence, Combinign both statements, we know that AC is perpendicular and that it bisects the non-equal side. Hence it should be an Isoceles triangle.

Its good to remember this rule. Just in case you want to know the proof:

Let triangle PQR, PQ = PR and QR is non equal side.
Now, Draw a perpendicular from P to line QR.
Let us name the point on QR as S.
now, Triangles, PQS and PRS are Congruent triangles.
Why?
becasue angle(PSQ)=angle(PSR), angle(PQS)=angle(PRS) and PQ = PR
by SAS property, both triangles are congruent.

Hence, QS = RS


Hope this helps!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
Post new topic Post Reply
• Page 1 of 1