In continuation of the CHSL study plan, we will discuss one of the important topics from the Geometry section i.e., " Important Theorems Related to Triangle ". Questions based on these theorems are frequently asked in the exam.
BASIC PROPORTIONALITY THEOREM
In a triangle, a line drawn parallel to one side to intersect the other side in distinct points divides the two sides in the same ratio
As per the basic proportionality theorem:
Mid-point Theorem
Mid-point theorem is a special case of " Basic Proportionality Theorem ". In the above triangle, D and E are the midpoints of the sides AB and AC respectively.
Then, as per the midpoint theorem
DE is parallel to BC, and
DE = 1/2 BC
Pythagoras Theorem
In right triangles, the square of the hypotenuse equals the sum of the squares of the other two sides
As per the Pythagoras theorem: AC2 = AB2 + BC2
It is important to learn the triplets that make right-angled triangles.
3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
9, 40, 41
11, 60, 61
12, 35, 37
16, 63, 65
20, 21, 29
These triplets satisfy the condition of AC2 = AB2 + BC2
If a, b, c denote the sides of a triangle then
- If c2 < a2 + b2, triangle is acute-angled.
- If c2 = a2 + b2, triangle is right angled.
- If c2 > a2 + b2, triangle is obtuse-angled
Median: A median of a triangle is the line from a vertex to the midpoint of the opposite side. The centroid is the point at which the medians of the triangle meet. The centroid divides the medians in the ratio 2:1. The median bisects the area of the triangles.
Theorem of Apollonius
Sum of the squares of two sides of a triangle
= 2 (median) 2 + 2 (half the third side)2
In the figure AD is the median, then: AB2 + AC2 =2(AD)2 + 2(BD)2
Angle Bisector Theorem
If AD is the bisector of angle A,
Then, AB/AC = BD/DC
Attempt the SSC CHSL Mega Mock Challenge for the upcoming SSC CHSL Tier-1 Exam and increase your chances of selection: Click Here
More from us:
BYJU'S Exam Prep brings to Online Classroom Program, which gives you Unlimited Access to All 18+ Structured Live Courses and 550+ Mock Tests.
Online Classroom Program Benefits:
- Structured Live Courses with Daily Study Plan
- Full syllabus coverage of {9+ SSC & Railway Exams} with live classes, study notes and interactive quizzes. (SSC CGL, CHSL, CPO, MTS, Delhi Police, RRB NTPC, Group D, & other govt. exams)
- Prepare with India's best Faculty with a proven track record
- Complete Doubt Resolution by Mentors and Experts
- Performance analysis and Report card to track improvement
Attempt subject wise questions in our new practise section' Click here
Download Gradeup, the best government exam app for Preparation
BYJU'S Exam Prep today to score better!!!
Comments
write a comment