Mid Point Theorem a complete explanation - Future Study Point

# MidPoint Theorem Complete Explanation

Midpoint theorem is compulsory in maths subject class 9 of each board wether it is CBSE or any other state boards. The questions based on mid point theorem are asked every year in CBSE class 9 half-yearly and annual exams.  Here in our website future study point, you can study NCERT solutions of maths and science, most important questions of maths and science, sample papers, guess papers, useful articles on science and maths for your preparation of SA1 and SA2 exams, articles on your carrier and other educational posts and topics related to the carrier in online jobs. If you like this post then please fill up our membership form so that you could get updated information on your mobile regarding our new posts. Here in this post, the verification of the midpoint theorem is completely explained by the expert so that you could do the solution of every question based on it.

Before you study midpoint theorem let’s go through the syllabus of CBSE class IX maths which has the lessons, number system, the lessons in algebraic part are polynomial, linear equations in two variable, coordinate geometry part contains only one lesson, the lessons in geometry part are the introduction to Euclid’s geometry, lines, and angle, triangles, quadrilaterals, area of quadrilateral and triangles, circles and construction. Here one of the most important parts is geometry. In CBSE IX class geometry the midpoint theorem is taken from lesson number 3 ‘Triangle’.  The midpoint theorem is one of the properties of the triangle, among all the theorem midpoint theorem, is the most important theorem. If you go through the last year’s question papers of maths you could see one or two questions based on midpoint theorem have been asked by the CBSE board every year. Midpoint theorem is based on the triangle which states that the line segment joining midpoints of two sides of the triangle is parallel to the third side and the line segment is half of the third side.

## MidPoint Theorem Complete Explanation

You can also study NCERT Solutions for class 9 maths Chapter 7-Triangles

NCERT Solutions:Chapter 7-Triangles

### Midpoint theorem-Prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side.

#### Given:

ΔABC in which E and F are midpoints of AB and AC respectively.

#### To prove:

EF∥BC & EF = BC/2

Construction:

Drawing CD∥AB and extending the line segment EF such that CD and EF intersect at D.

Proof:

CF = AF     (Midpoint of AC)

∠DCF = ∠FAE   (Alternative angles)

∠AEF = ∠FDC (Alternative angles)

ΔAEF ≅ ΔCDF (AAS rule)

∴ AE = DC   ( By CPCT)

AE= BE   (Midpoint of AB)

So,DC = BE

DC = BE and DC∥ BE, If one set of opposite sides of a quadrilateral are equal and parallel then it is a parallelogram.

Therefore BCDE is a parallelogram

∴ BC∥ DE and thus

EF ∥ BC, Hence proved

Since we have proved above ΔAEF ≅ ΔCDF

EF = DF (By CPCT)

DE = BC (It has been proved above BCDE is a parallelogram)

EF + DF = DE

2EF = DE

2EF = BC

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#### The converse of midpoint theorem:

If a line is drawn through the midpoint of a side of the triangle which is parallel to another side then this line bisects the third side of the triangle.

In ΔPQR if T is the midpoint of PQ and TS∥ QR, then TS bisects PR

## NCERT Solutions of Science and Maths for Class 9,10,11 and 12

### NCERT Solutions for class 9 maths

 Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles Chapter 2-Polynomial Chapter 10-Circles Chapter 3- Coordinate Geometry Chapter 11-Construction Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes Chapter 6-Lines and Angles Chapter 14-Statistics Chapter 7-Triangles Chapter 15-Probability Chapter 8- Quadrilateral

### NCERT Solutions for class 9 science

 Chapter 1-Matter in our surroundings Chapter 9- Force and laws of motion Chapter 2-Is matter around us pure? Chapter 10- Gravitation Chapter3- Atoms and Molecules Chapter 11- Work and Energy Chapter 4-Structure of the Atom Chapter 12- Sound Chapter 5-Fundamental unit of life Chapter 13-Why do we fall ill ? Chapter 6- Tissues Chapter 14- Natural Resources Chapter 7- Diversity in living organism Chapter 15-Improvement in food resources Chapter 8- Motion Last years question papers & sample papers

### NCERT Solutions for class 10 maths

 Chapter 1-Real number Chapter 9-Some application of Trigonometry Chapter 2-Polynomial Chapter 10-Circles Chapter 3-Linear equations Chapter 11- Construction Chapter 4- Quadratic equations Chapter 12-Area related to circle Chapter 5-Arithmetic Progression Chapter 13-Surface areas and Volume Chapter 6-Triangle Chapter 14-Statistics Chapter 7- Co-ordinate geometry Chapter 15-Probability Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

### NCERT Solutions for Class 10 Science

 Chapter 1- Chemical reactions and equations Chapter 9- Heredity and Evolution Chapter 2- Acid, Base and Salt Chapter 10- Light reflection and refraction Chapter 3- Metals and Non-Metals Chapter 11- Human eye and colorful world Chapter 4- Carbon and its Compounds Chapter 12- Electricity Chapter 5-Periodic classification of elements Chapter 13-Magnetic effect of electric current Chapter 6- Life Process Chapter 14-Sources of Energy Chapter 7-Control and Coordination Chapter 15-Environment Chapter 8- How do organisms reproduce? Chapter 16-Management of Natural Resources

### NCERT Solutions for class 11 maths

 Chapter 1-Sets Chapter 9-Sequences and Series Chapter 2- Relations and functions Chapter 10- Straight Lines Chapter 3- Trigonometry Chapter 11-Conic Sections Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry Chapter 5-Complex numbers Chapter 13- Limits and Derivatives Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning Chapter 7- Permutations and Combinations Chapter 15- Statistics Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

### NCERT Solutions for Class 11 Physics

Chapter 1- Physical World

chapter 3-Motion in a Straight Line

### NCERT Solutions for Class 11 Chemistry

Chapter 1-Some basic concepts of chemistry

Chapter 2- Structure of Atom

### NCERT Solutions for Class 11 Biology

Chapter 1 -Living World

### NCERT solutions for class 12 maths

 Chapter 1-Relations and Functions Chapter 9-Differential Equations Chapter 2-Inverse Trigonometric Functions Chapter 10-Vector Algebra Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry Chapter 4-Determinants Chapter 12-Linear Programming Chapter 5- Continuity and Differentiability Chapter 13-Probability Chapter 6- Application of Derivation CBSE Class 12- Question paper of maths 2021 with solutions Chapter 7- Integrals Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution

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