GMAT Math : Triangle sufficiency

Let’s start with a GMAT Data sufficiency example:

What is the area of the triangle ABC?

  1. Two of the sides measure 10 cm and 15 cm and the angle between them measure 300
  2. One of the sides measures 10 cm and 2 of the angles touching it measure 300 and 400

Readers are encouraged to take some time to tackle the above question 🙂

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The above question relates to congruence of triangles. Let’s do a quick refresher:

Congruence of triangles: As long as certain dimensions of a triangle are given, we can determine ALL other dimensions (lengths and angles) of the triangle.

The certain dimensions given can essentially be in 4 forms:

1. Side – Angle – Side : Two side lengths and the angle between them

2. Angle – Side – Angle : Two angles and the side length between them

3. Angle – Side – Side : One angle and the sides lengths as shown below. Important : We need to know which side the angle connectsthis is a key requirement for this bucket

4. Side – Side – Side : All the side lengths are given

5. Hypotenuse – Side : Length of hypotenuse and one of the other sides in a right triangle

Reader’s will note this case is just a variation of Angle – Side – Side :  We already know the angle is 90 degrees

Essentially, if 1 of these ‘sets’ of information is given, ALL the other sides and angles can be determined for the particular triangle. And by knowing all the sides of a triangle we can calculate its area rather quickly using Heron’s formula

Coming back the original question, the first statement gives us Side – Angle – Side and is sufficient by itself and the second statement gives us Angle – Side – Angle and is sufficient independently as well

We go with option (D)

Challenge question: What if one of the statements given was “Two of the sides measure 10 and 15 cm and one of the angles measure 300”. Would this also be independently sufficient?

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The answer is No. For congruence to work, we need to know the ‘relative positioning’ of the angle.

We need to know if the data given is Side – Angle – Side or Angle – Side – Side and in the case of Angle – Side – Side which Side the angle is connected to.

Find Data sufficiency challenging? For more comprehensive tips on Q50+ Data sufficiency, do check out our guide here