Geometry

Basics of geometry including concepts of triangles, similar triangles, quadrilaterals, polygons and circles are oft repeated questions both in the GMAT Problems Solving section and in the GMAT Data Sufficiency section of the GMAT Math Section. A good grasp of the fundamentals of Geometry will help you crack questions from this topic with relative ease. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts:

1. Definition of various terms used in geometry
2. Properties of concepts explained, with illustrations
3. Detailed explanation of the concepts in angles
4. Introduction into triangles and related properties with illustrative examples
5. Different types of triangles
6. Concepts and theorems, such as Apollonius Theorem and Pythagoras Theorem, associated with triangles with illustrative examples
7. Explanation of relationship between area of triangles, inradius and circumradius
8. Introduction of different polygons, meaning of quadrilaterals, squares, rectangles, rhombus, parallelogram, kite and trapezium
9. Circles and various associated concepts and properties, with illustrative examples
10. Different types of circles
11. 22 solved examples with illustrations
12. 13 exercise problems with the answer key and explanatory answers

Here is an example of a typical solved example in this chapter.
Sample Question
Question
In a TriangleABC. AB = 4.5, AC = 6 and BC = 7.5. The points D & E lie on the line segment BC with BD = 1.5 and EC = 3. What is the value of the /_DAE?

Explanatory Answer
Geometry Solved Example - Solution Image The triangle is right-angled (4.5, 6 and 7.5).
Therefore /_A is right-angled.
BD = 1.5, EC = 3 => BE = 4.5 and DC = 6
Hence AB = BE = 4.5 and AC = CD = 6 and
Therefore
/_BAE = /_BEA = /_DEA and /_DAC = /_ADE
In triangle ADE, /_ADE + /_DEA + /_DAE = 180o
=> /_DAC + /_BAE + /_DAE = 180o
=> (90o + /_DAE) + /_DAE = 180o
=> /_DAE = 45o