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QonABand AC respectively so that AP = DE andAQ = DF. Join PandQ. Proof: Steps Justificaltin (1) In 'APQ and 'DEF ,AP DE, AQ DF a ...

? ‘BAG ‘EDH (3) because'ABC and 'DEF are similar. EF BC DE AB p h 2 2 EF BC EF BC EF BC EF BC p h DEF ABC u u ' ' ? [Triangles A ...

Exercise 14⋅ 2 Consider the following information: i. ratios are considered to compare two expressions ii. to find ratio, expre ...

2 2 2 2 2 2 EF BC DF AC DE AB DEF ABC ' ' In the triangles ABC and DEF‘A =‘D. Prove that, 'ABCt'DEF AB.ACtDE.DF. The bisector A ...

polygon made up of the least number of line segments. An equilateral triangle is a regular polygon of three sides. An equilatera ...

0DWK,;;)RUPD Identify the lines of symmetry in the following geometrical figures: Complete each of the following incompl ...

Here is one more example for rotational symmetry. Consider the intersection of two diagonals of a square the centre of rotation. ...

Activity: Determine the line of symmetry and the rotational symmetry of the given alphabet and complete the table below: Letter ...

Chapter Fifteen Area Related Theorems and Constructions We know that bounded plane figures may have different shapes. If the reg ...

When the area of two regions are equal, the sign ‘=’ is used between them. For example, in the figure the area of the rectangula ...

Theorem 2 Parallelograms lying on the same base and between the same pair of parallel lines are of equal area. Let the parallelo ...

Therefore, 'CAD#'FAB (2) Triangular region CADand rectangular regionADLMlie on the same base AD and between the parallel linesAD ...

Again, area of the parallelogram region ECGF is 2 (area of the triangular region AEC) [ since both lie on the same base and ECll ...

0DWK,;;)RUPD Construction: Join B,D. Through C construct CF parallel to DB which intersects the side AB extended at F. Fi ...

Prove that any median of a triangle divides the triangular region into two regions of equal area. A parallelogram and a rectang ...

Chapter Sixteen Mensuration The length of a line, the area of a place, the volume of a solid etc. are determined for practical p ...

Let in 'ABCthe sides are : BC a,CA b,AB c. AD is drawn perpendicular from A to BC. Let altitude (height) AD h. Considering the a ...

= a ac c a b a ac c a b 2 2 2 2 2 2 2 ^2 ^2 ^2 ˜    = 2 2 2 2 2 4 {( ) }{ ( )} a ca b b ca = 2 4 ( )( 2 )( 2 () 2 ) a ...

DrawADABC.? 2 b BD CD In 'ABD right angled ? 4 4 2 4 2 2 2 2 2 AD^2 AB^2 BD^2 a^2 b ̧ a b a b ¹ · ̈ ©  § ? 2 4 a^2 b^2 AD  ...

Solution : Let, the lengths of the sides of the triangle are a 7 cm., b 8 cm. and c 9 cm. ? Semi perimeter 2 7 8 9 2     a b ...