Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 1

Friday, June 2nd, 2017


Geometry Fundas-1

I got a lot of feedback via emails and texts that people are looking for a post on geometry. I have been avoiding it for sometime because of two main reasons:

a)      It is not one of my strong areas.

b)      It takes a lot of time to draw the diagrams that are sometimes required to explain the fundas.

The questions on geometry are the trickiest and consumes the maximum amount of time as compared to the questions on other topics in Quantitative aptitude that is why, I have compiled a list of fundas that you might find helpful in solving CAT level questions. I am splitting those in two posts so that one post does not become too long / intimidating. In this post, we will discuss Geometry fundas related to lines, triangles, parallelograms, trapeziums, polygons, etc.

You might find some of them very simple or ideas that are obvious to you. If that is the case, be glad that your preparation is up to the mark. If not, then be glad you got them in time. (Yes – I am inspired by two-face J)

Funda 1:

1

The ratio of intercepts formed by a transversal intersecting three parallel lines is equal to the ratio of corresponding intercepts formed by any other transversal.

2

Funda 2:

Centroid and Incenter will always lie inside the triangle. About the other points:

–          For an acute angled triangle, the Circumcenter and the Orthocenter will lie inside the triangle.

–          In case of an obtuse angled triangle, the Circumcenter and the Orthocenter will lie outside the triangle.

–          and right-angled triangle, the Circumcenter will lie at the midpoint of the hypotenuse and the Orthocenter will lie at the vertex at which the angle is 90°.

 Funda 3:

The orthocentercentroid, and circumcenter always lie on the same line known as Euler Line.

–          The orthocenter is twice as far from the centroid as the circumcenter is.

–          If the triangle is Isosceles then the incenter lies on the same line.

–          If the triangle is equilateral, all four are the same point.

Funda 4:

Appolonius’ Theorem {AD is the median}

3

AB2 + AC2 = 2 (AD2 + BD2)

 Funda 5: For cyclic quadrilaterals –

Area =  where s is the semi perimeter

Also, Sum of product of opposite sides = Product of diagonals

Funda 6:

If a circle can be inscribed in a quadrilateral, its area is given by =

4

Funda 7:

Parallelograms

AC2 + BD2 = AB2 + BC2 + CD2 + DA2

 

Funda 8:Trapeziums

AC2 + BD2 = AD2 + BC2 + 2 x AB x CD

 

Funda 9:

I will wrap up this post here. In my next and final post on Geometry we will discuss fundas related to circles (specifically – common tangents), solid figures, mensuration and co-ordinate geometry.

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Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 2

Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 1
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One response to “Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 1”

  1. […] the previous post we discussed lines, triangles, parallelograms, trapeziums, polygons etc. Now, we will discuss other […]

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