CBSE Class 9 | Triangles on the same Base and between the same Parallels are equal in area

All these solutions are based on geomentry,properties of triangles and intended to use Parallelogram Theorems.Students can learn to solve problems on Areas of Parallelograms and Triangles.

http://www.learncbse.in/ncert-solutions-for-class-9-maths/

Area of a figure is a number (in some unit) associated with the part of the plane enclosed by that figure.

Two figures are called congruent, if they have the same shape and the same size.

How to recognise Figures on the Same Base and Between the Same Parallels

All these solutions are based on geomentry,properties of triangles and intended to use Parallelogram Theorems.Students can learn to solve problems on Areas of Parallelograms and Triangles.

http://www.learncbse.in/ncert-solutions-for-class-9-maths/

Area of a figure is a number (in some unit) associated with the part of the plane enclosed by that figure.

Two figures are called congruent, if they have the same shape and the same size.

How to recognise Figures on the Same Base and Between the Same Parallels

00:02CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q7. D and E are points on sides AB and AC respectively of triangle ABC such that ar (DBC) = ar (EBC). Prove that DE || BC.

01:35 Find Area of Triangle:Area of a triangle is half the product of its base (or any side ) and the corresponding altitude (or height)

02:25 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q8. XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively, show that ar (ABE) = ar (ACF)

04:20 Apply Propeerties of Parallelogram

10:14 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q9. The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see Fig. 9.26). Show that ar (ABCD) = ar (PBQR).[ Hint : Join AC and PQ. Now compare ar (ACQ) and ar (APQ).]

11:26 Apply Prallelogram Theorem:If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.

13:49 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q10. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O.Prove that ar (AOD) = ar (BOC).

15:23 Apply Prallelogram Theorem:Triangles on the same base (or equal bases) and between the same parallels are equal in area.

16:18 Q11. In Fig. 9.27, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that (i) ar (ACB) = ar (ACF) (ii) ar (AEDF) = ar (ABCDE)

17:59 Use Prallelogram Theorem:Triangles on the same base (or equal bases) and between the same parallels are equal in area

19:35 Q13. ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY). [ Hint : Join CX.]

20:07 Procedure for construction to solve the problem.

21:42 Triangle Theorem:Two triangles on the same base(or equal bases) and between the same parallels are equal in area .

23:29 Q14. In Fig.9.28, AP || BQ || CR. Prove that ar (AQC) = ar (PBR).

24:24 Triangle Theorem:

23:16 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q15. Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

26:37 Constructions steps

27:50 Use Triangle Theorem:Two triangles on the same base(or equal bases) and between the same parallels are equal in area

28:34 Property of Trapezium:The bases (top and bottom) of an isosceles trapezoid are parallel. Opposite sides of an isosceles trapezoid are the same length.

28:40 CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles Q16. In Fig.9.29, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

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CBSE solutions for class 9 maths Areas of Parallelograms and Triangles

CBSE class 9 maths chapter 10 Areas of Parallelograms and Triangles

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