We have covered the important topics of Quantitative Aptitude Section such as Arithmetic and Algebra. But, now it’s time that we move ahead and learn the concepts of Geometry.
It is expected that Geometry and Mensuration will section will carry approximately 8-10 questions. As the trend analysis of the CAT paper shows 98% questions from geometry section are based on the simple geometrical formulas.
So a basic understanding of these concepts would make your job easy in handling the questions from this section. Let us take an in-depth overview of these concepts to crack the exam easily.
Parallel lines: Two lines are parallel if they line on the same plane and never intersect.
Transversal: When a straight line intersects two parallel lines as shown below, then it satisfies the following conditions:
Triangles: A triangle is a polygon with three sides.
- The sum of its interior angles is 1800
- The angle opposite to the longest side of the triangle will have the greatest angle and the angle opposite to the shortest side of the triangle will have the smallest angle.
- The sum of two sides of a triangle is greater than the third angle of the triangle.
- The difference between the two angles of a triangle is smaller than the third angle of the triangle.
Types of triangle:
Area of a triangle:
Angle bisector: Any line that divides the angle of a vertex into two equal halves is called as the angle bisector.
- Incenter: All the three angle bisectors meet at a particular point called Incenter. Incenter is also the centre of the incircle that is inscribed in a triangle touching all the sides of it.
Mid-point theorem: The line joining the mid-points of two sides of a triangle is parallel to the third side. The parallel line is also half in distance than the third side.
Thales theorem: A line parallel to any side of the triangle divides the other two sides proportionally.
In the figure below,
Arc: An arc is a part of the circumference of the circle. The bigger part of the arc is the major arc and the smaller one is the minor arc.
Where r is the radius of the circle
Sector: It is the area covered by an arc.
Segment: The area below the triangle formed by the sector is the segment.
Chord: A chord is a line segment with its end points on the circle.
- Diameter is the longest chord of a circle.
- Chords equidistant from the center are equal.
- Chords of equal distance subtend equal angles at the center.
- Angle subtended by a chord/arc at the center is twice that subtended at the circumference of the circle.
- Perpendicular bisector of a chord always passes through the center of the circle.
Tangent: Tangent to a circle is a line which has only one point of contact at the circumference of a circle.
- A tangent is always perpendicular to radius.
- Any point external to the circle can have only two tangents that are equal.
Alternate segment theorem: Angle made by a chord with a tangent to the circle is equal to the angle subtended by the chord in the opposite side of the circumference.
Polygons: Polygons are closed figures formed by a series of linear segments.
- Regular polygons: Polygons with equal sides and angles.
- Irregular polygons: Polygons with unequal sides and angles.
- Convex polygon: If none of the interior angles is more than 1800, then the polygon is convex.
- Concave polygon: If any one of the interior angles is more than 1800, then the polygon is concave.
Some important points:
Some basic characteristics of different polygons:
Also Take: Practice Test of Geometry
We hope that these concepts along with their related exercises will aid you in your preparation of Geometry chapter.
Share with us your queries in case we missed on some important concept of this chapter. You can also share this article with your friends if they are looking for some help in the Geometry section for preparation.
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