Let’s start with a GMAT Data sufficiency example:

**What is the area of the triangle ABC?**

**Two of the sides measure 10 cm and 15 cm and the angle between them measure 30**^{0}**One of the sides measures 10 cm and 2 of the angles touching it measure 30**^{0}and 40^{0}

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 connects – this 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 30^{0}”. 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