Mid Point Theorem a complete explanation - Future Study Point

Mid Point Theorem a complete explanation

Midpoint theorem

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.

Midpoint theorem



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.

midpoint theorem



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

To prove:

EF∥BC & EF = BC/2


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


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

In the quadrilateral BCDE

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


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.

mid point theorem pic 3



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 SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 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 equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 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 FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE 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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