Selina Class 9 ICSE Solutions Mathematics : Chapter 12- Mid-point and Its Converse [ Including Intercept Theorem]

Class 9: Maths Chapter 12 solutions. Complete Class 9 Maths Chapter 12 Notes.

Selina Class 9 ICSE Solutions Mathematics : Chapter 12- Mid-point and Its Converse [ Including Intercept Theorem]

Selina 9th Maths Chapter 12, Class 9 Maths Chapter 12 solutions

Exercise 12(A)

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Solution 12:

Solution 13:

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Solution 17:

Exercise 12(B)

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Solution 12:
Given ABCD is parallelogram, so AD = BC, AB = CD.
Consider triangle APB, given EC is parallel to AP and E is midpoint of side AB. So by midpoint theorem, C has to be the midpoint of BP.
So BP = 2BC, but BC = AD as ABCD is a parallelogram.
Hence BP = 2AD
Consider triangle APB, AB || OC as ABCD is a parallelogram. So by midpoint theorem, O has to be the midpoint of AP.
Hence Proved

Solution 13:
Consider trapezium ABCD.
Given E and F are midpoints on sides AD and BC, respectively.


Consider LHS,
AB + CD = AB + CJ + JI + ID = AB + 2HF + AB + 2EG
So AB + CD = 2(AB + HF + EG) = 2(EG + GH + HF) = 2EF
AB + CD = 2EF
Hence Proved

Solution 14:
Given Δ ABC
AD is the median. So D is the midpoint of side BC.
Given DE || AB. By the midpoint theorem, E has to be midpoint of AC.
So line joining the vertex and midpoint of the opposite side is always known as median. So BE is also median of Δ ABC.

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Selina Class 9 ICSE Solutions Mathematics : Chapter 12- Mid-point and Its Converse [ Including Intercept Theorem]

Download PDF: Selina Class 9 ICSE Solutions Mathematics : Chapter 12- Mid-point and Its Converse [ Including Intercept Theorem] PDF

Chapterwise Selina Publishers ICSE Solutions for Class 9 Mathematics :

• Chapter 1 – Rational and Irrational Numbers
• Chapter 2- Compound Interest (Without using formula)
• Chapter 3 – Compound Interest (Using Formula)
• Chapter 4- Expansions (Including Substitution)
• Chapter 5- Factorisation
• Chapter 6 – Simultaneous (Linear) Equations (Including Problems)
• Chapter 7- Indices (Exponents)
• Chapter 8- Logarithms
• Chapter 9- Triangles [Congruency in Triangles]
• Chapter 10- Isosceles Triangles
• Chapter 11- Inequalities
• Chapter 12- Mid-point and Its Converse [ Including Intercept Theorem]
• Chapter 13- Pythagoras Theorem [Proof and Simple Applications with Converse]
• Chapter 14- Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
• Chapter 15- Construction of Polygons
• Chapter 16- Area Theorems [Proof and Use]
• Chapter 17- Circle
• Chapter 18- Statistics
• Chapter 19- Mean and Median
• Chapter 20 – Area and Perimeter of Plane Figures
• Chapter 21- Solids [Surface Area and Volume of 3-D Solids]
• Chapter 22- Trigonometrical Ratios
• Chapter 23- Trigonometrical Ratios of Standard Angles
• Chapter 24- Solution of Right Triangles
• Chapter 25- Complementary Angles
• Chapter 26- Co-ordinate Geometry
• Chapter 27- Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)
• Chapter 28- Distance Formula

About Selina Publishers ICSE

Selina Publishers has been serving the students since 1976 and is one of the quality ICSE school textbooks publication houses. Mathematics and Science books for classes 6-10 form the core of our business, apart from certain English and Hindi literature as well as a few primary books. All these books are based upon the syllabus published by the Council for the I.C.S.E. Examinations, New Delhi. The textbooks are composed by a panel of subject experts and vetted by teachers practising in ICSE schools all over the country. Continuous efforts are made in complying with the standards and ensuring lucidity and clarity in content, which makes them stand tall in the industry.