Class name Subject Book title Chapter number Content Created at
Class VII Mathematics Ganita Prakash-II 1 cm, and 80 cm, suppose the sidelengths had been 4 cm, 6 cm, 8 cm (this triangle can fit on our page). Is this information sufficient to replicate t...
Class VII Mathematics Ganita Prakash-II 1 there other ways of overlapping the vertices so that the triangles fit exactly over each other? The fact that these triangles are congruent shows t...
Class VII Mathematics Ganita Prakash-II 1 Prakash | Grade 7 | Part-II A A 80° A 80° 80° B 30° 70° B 30° 70° C B 30° 70° C C These triangles are seen to have the same shape, but not the same...
Class VII Mathematics Ganita Prakash-II 1 3: Draw a sufficiently long arc from Q of radius 4 cm cutting the line l. l S R 30° Q P 6 cm How do we find the required triangle from this figure?...
Class VII Mathematics Ganita Prakash-II 1 (as O is the midpoint of BC). Are there any other equal sides or angles? We also have, ∠AOB = ∠DOC, as they are vertically opposite angles. We see ...
Class VII Mathematics Ganita Prakash-II 1 4 cm Fig.1.2 How do we proceed with this problem? Here is a method. What are the measures of ∠B and ∠Y? We know that the sum of the angles of a tri...
Class VII Mathematics Ganita Prakash-II 1 the line l. Join PR. P Q 4 cm R ΔPQR is the required triangle. 16 Geometric Twins Consider the downward extension of line l below QR. Would the arc...
Class VII Mathematics Ganita Prakash-II 1 Thus, the triangles satisfy the RHS condition. Hence, Δ ADB ≅ ΔADC. Thisshowsthat∠B=∠C,astheyarecorrespondingpartsofcongruent triangles. Thus, the ...
Class VII Mathematics Ganita Prakash-II 1 = ED (c) AB = DF (d) ∠A = ∠D ∠B = ∠D = 90° ∠B = ∠E AC = FE AC = DF (e) AB = DF ∠B = ∠F AC = DE 3. It is given that OB = OC, and OA = OD. Show that ...
Class VII Mathematics Ganita Prakash-II 1 triangle are equal to the two sides and the included angle of another triangle, we say that the SAS (Side Angle Side) condition is satisfied. The S...
Class VII Mathematics Ganita Prakash-II 2 OPERATIONS WITH INTEGERS 2.1 A Quick Recap of Integers Rakesh’s Puzzle: A Number Game Rakesh gives you a challenge. “I have thought of two numbers”...
Class VII Mathematics Ganita Prakash-II 2 coin is struck to move it to the right. Each strike moves the coin a certain number of units of distance rightwards based on the force of the strik...
Class VII Mathematics Ganita Prakash-II 2 negative integers. First, let us model the line on which the coin moves as a number line. –ve +ve . .–5 –4 –3 –2 –1 0 1 2 3 4 5 6 . . . Let us cons...
Class VII Mathematics Ganita Prakash-II 2 to each other, and what are their directions? This Remember to start from 0. 1. b a –ve P 0 +ve 2. a b –ve 0 P +ve 3. a b –ve 0 +ve P 27 Ganita Pra...
Class VII Mathematics Ganita Prakash-II 2 represent addition and subtraction of integers. We now explore how to model multiplication of integers using tokens. Suppose we put some positive t...
Class VII Mathematics Ganita Prakash-II 2 need to do this 4 times. Remove 2greentokens fromthe zeropairs, 4times (–  4)=–  8 After removing the positives, 8 negatives are left in the bag. T...
Class VII Mathematics Ganita Prakash-II 2 0 × (–3) = 0 This is the inverse of the previous pattern. When the multiplicand is negative,foreveryunitdecreaseofthemultiplier,theproductincreases...
Class VII Mathematics Ganita Prakash-II 2 –3 = 21 8 × 3 = 24 –8 × 3 = –24 8 × –3 = –24 –8 × –3 = 24 9 × 3 = 27 –9 × 3 = –27 9 × –3 = –27 –9 × –3 = 27 10 × 3 = 30 –10 × 3 = –30 10 × –3 = –30...
Class VII Mathematics Ganita Prakash-II 2 same when we swap the multiplier and the multiplicand? Try this for some numbers. Observethefollowingpairsofmultiplications(fillintheblankswhere ne...
Class VII Mathematics Ganita Prakash-II 2 (18.30-32), Brahmagupta wrote: “The product or quotient of two fortunes is a fortune. The product or quotient of two debts is a fortune. The produc...
Class VII Mathematics Ganita Prakash-II 2 its position after 45 minutes? Solution: Solution to part (a) of the question: Method 1: We can model this using subtraction. The elevator moves at...
Class VII Mathematics Ganita Prakash-II 2 (– 46) ÷ (– 23) 2. A freezing process requires that the room temperature be lowered from 32°C at the rate of 5°C every hour. What will be the room ...
Class VII Mathematics Ganita Prakash-II 2 × b) × c. In the expression 5 × – 3 × 4, try to multiply 5 and 4 first and then multiply the product with – 3: (5 × 4) × – 3. 5 × 4 = 20, and 20 × ...
Class VII Mathematics Ganita Prakash-II 2 objects to visually understand why the distributive property holds. We can use the same setup even in the case of integers by using green tokens fo...
Class VII Mathematics Ganita Prakash-II 2 2. Find the values of the following expressions: (a) (– 27) ÷ 9 (b) 84 ÷ (– 4) (c) (– 56) ÷ (– 2) 3. Find the integer whose product with (– 1) is: ...