Triangles Question - Manhattan 5lb

GRE Quant Problem Solving
1

I was doing the below question from the Manhattan 5lb book (Triangles chapter) and I realized that there are 2 ways to solve this:

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Angle ABD = 180-2x (supplementary angles) and hence angle ADB =x.

Approach 1: We can see that angle x is opp to AB and angle 2x is opp to DC. 2x> x so DC>AB and hence choose (A)

Approach 2: If we use the isosceles triangle property, then AB=BD (as angle DAB=ADB=x). Since angle DBC= angle DCB, so BD=DC. Therefore, AB=BD=DC so go with ( C ).

Manhattan has given the second approach in their answer guide. I thought of both the approaches and ended up choosing (D) because of conflicting answers. Iā€™m sure I am missing some concept. Could someone explain why my 1st approach is wrong?

1 Like
2

Hi,the approach 1 is incorrect because this correponding relationship between angle and side is only applied to the situation in which angles and sides are in the same triangle. As you can see, in triangle ADC, the length of AD is twice the length of side of DC. That proved the above-mentioned rule is not broken.

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Ah yes! Thank you! I knew I was missing some part of the concept.