Category: ICSE

ML Aggarwal Class 7 Solutions Chapter 16 Perimeter and Area Ex 16.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Ex 16.2

Question 1.
Find the area of each of the following parallelogram:

Solution:

Question 2.
Find the area of each of the following triangles:

Solution:

Question 3.
Find the missing values:

Solution:

Question 4.
Find the missing values:

Solution:

Question 5.
In the given figure, ABCD is a parallelogram whose two adjacent sides are 6 cm and 4 cm. If the height corresponding to the base AB is 3 cm, find:
(i) the area of parallelogram ABCD
(ii) the height corresponding to the base AD.

Solution:

Question 6.
In the given figure, ABC is an isosceles triangle with AB = AC = 7.5 cm and BC = 9 cm. If the height AD from A to BC is 6 cm, find:
(i) the area of ∆ABC
(ii) the height CE from C to AB.

Solution:

Question 7.
If the base of a right-angled triangle is 8 cm and the hypotenuse is 17 cm, find its area.
Solution:

Question 8.
In the given figure, ∆ABC is right-angled at B. Its legs are 8 cm and 6 cm. Find the length of perpendicular BN on the side AC.

Solution:

Question 9.
In the given figure, the area of ∆ABE is equal to the area of parallelogram ABCD. If altitude EF is 16 cm long, find the length of the altitude of the parallelogram to the base AB of length 10 cm. What is the area of ∆AMD, where M is mid-point of side DC?

Solution:

Question 10.
In the given figure, ABCD is a rectangle of size 18 cm by 10 cm. In ABEC, ∠E = 90° and EC = 8 cm. Find the area of the shaded region.

Solution:

Question 11.
In the following figures, find the area of the shaded regions:

Solution:

ML Aggarwal Class 7 Solutions Chapter 11 Triangles and its Properties Ex 11.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1

Question 1.
In the adjoining figure:

(i) Name the vertex opposite to side PQ.
(ii) Name the side opposite vertex Q.
(iii) Name the angle opposite to side QR.
(iv) Name the side opposite to ∠R.
Solution:

Question 2.
Look at the figures given below and classify each of the triangles according to its (a) sides (b) angles
(You may judge the nature of the angle by observation):

Solution:

Question 3.
In the given ∆PQR, if D is the mid-point of \(\bar { QR }\), then
(i) \(\bar { PM }\) is ……..
(ii) \(\bar { PD }\) is ………
Is QM = MR?

Solution:

Question 4.
Will an altitude always lie in the interior of a triangle? If no, draw a rough sketch to show such a case.
Solution:

Question 5.
Can you think of a triangle in which two altitudes of the triangle is its sides? If yes, draw a rough sketch to show such a case.
Solution:

Question 6.
Draw rough sketches for the following:
(i) In ∆ABC, BE is a median of the triangle.
(ii) In ∆PQR, PQ and PR are altitudes of the triangle.
(iii) In ∆XYZ, YL is an altitude in the exterior of the triangle.
Solution:

Question 7.
Take an equilateral triangle and draw its medians and altitudes and check that the medians and altitudes are the same.
Solution:

ML Aggarwal Class 7 Solutions Chapter 10 Lines and Angles Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 10 Lines and Angles Check Your Progress

Question 1.
Find the supplementary angle of each of the following angles:
(i) \(\frac { 1 }{ 2 }\) of 90°
(ii) \(\frac { 3 }{ 7 }\) of 280°
Solution:

Question 2.
How many degrees are there in an angle which is one-fifth of its complement?
Solution:

Question 3.
If two angles are supplementary and one angle is 5° more than four times the other, find the angles.
Solution:

Question 4.
The given diagram shows two intersecting straight lines. Find the values of x, y and z.

Solution:

Question 5.
In the given diagram, lines AB and CD intersect at O. If ∠1 + ∠3 = 78°, find the size of ∠2.

Solution:

Question 6.
(a) In the figure (i) given below, l || m. If ∠5 = 65°, find all other angles.
(b) In the figure (ii) given below, l || m. Find the values of x, y and z.
(c) In the figure (iii) given below, l || m and p || q. Find the values of x, y and z.

Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Check Your Progress

Question 1.
Consider the expression \(\frac { 3 }{ 2 }\) x²y – \(\frac { 1 }{ 2 }\) xy² + 6x²y².
(i) How many terms are there? What do you call such an expression?
(ii) List out the terms.
(iii) In the term \(\frac { -1 }{ 2 }\) xy², write down the numerical coefficient and the literal coefficient.
(iv) In the term \(\frac { -1 }{ 2 }\) xy², what is the coefficient of x?
Solution:

Question 2.
Write the Degree of the following polynomials:
(i) \(\frac { 2 }{ 5 }\) x³ – 7x² – \(\frac { 1 }{ 2 }\) x + 3
(ii) \(\frac { 2 }{ 3 }\) xy² – 5xy + \(\frac { 3 }{ 5 }\) y²x² + 2x
Solution:

Question 3.
Identify monomials, binomials and trinomials from the following algebraic expressions:
(i) 5x × y
(ii) 3 – 5x
(iii) \(\frac { 1 }{ 2 }\) (7x – 3y + 5z)
(iv) 3x² – 1.2xy
(v) -3x³y⁴z⁵
(vi) 5x(2x – 3y) + 7x²
Solution:

Question 4.
Using horizontal method:
(i) Add x² + y² – 2xy, -2x² – y² – 2xy and 3x² + y² + xy
(ii) Subtract -x² + y² + 2xy from 2x² – 3y².
Solution:

Question 5.
Using column method, add ab + 2bc – ca and 2ab – bc – ca and subtract 4ab + 5bc – 3ca.
Solution:

Question 6.
The sides fo a triangle are 5a – 3b, 3a + 2b and 5b – 2a, find its perimeter.
Solution:

Question 7.
If two adjacent sides of a rectangle are 4x +7y and 3y – x, find its perimeter.
Solution:

Question 8.
Subtract the sum of 3x² + 2xy – 2y² and 5y² – 7xy from 5x² + 2y² – 3xy.
Solution:

Question 9.
What must be added to 5x³ – 2x² + 3x + 7 to get 7x³ + 7x – 5?
Solution:

Question 10.
How much is 3p – 4q + r less than 4p + 3q – 5r?
Solution:

Question 11.
How much is 3a² – 5ab + 7b² + 3 greater than 2a² + 2ab + 5?
Solution:

Question 12.
How much should 5x³ + 3x² – 2x + 1 be increased to get 6x² + 7?
Solution:

Question 13.
Subtract the sum of 12ab – 10b² – 18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² – a².
Solution:

Question 14.
when a = 3, b = 0, c = -2, find the values of:
(i) ab + 2bc + 3ca + 4abc
(ii) a³ + b³ + c³ – 3abc
Solution:

Question 15.
Write the algebraic expression for the nth term of the number pattern 13, 23, 33, 43, ………..
Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) The terms with different algebraic factors are called ……….
(ii) The number of terms in a monomial is ………
(iii) An algebraic expression having two unlike terms is called a ……..
(iv) 3a²b and -7ba² are ……….. terms.
(v) -6a²b and -6ab² are ……… terms.
(vi) The number of unlike terms in the algebraic expression 3x² – 2xy + 5x² is ………
(vii) The factors of the term -3p²q² are ……..
(viii) The perimeter of a triangle whose sides measure 2a, b and a + b is ………
(ix) The value of the expression 2x³ – 7x² + 5x – 3 when x = 1 is ………..
(x) In the term -7a²bc, the coefficient of a is ……..
(xi) The degree of the polynomial 3 – 5x² + 7x³ – x⁴ is ……….
(xii) The degree of the polynomial 3x² – 2xy² + 5 is ………
Solution:

Question 2.
State whether the following statements are true (T) or false (F).
(i) The expression 5x + 7 – 2x is a trinomial.
(ii) (7x – 10) – (3x – 5) = 4x – 15.
(iii) The coefficient of 3x in -3x³y is -xy.
(iv) The constant term in the expression 2x² – 3xy – 7 is 7.
(v) If x = 3 and y = \(\frac { 1 }{ 3 }\) then the value of xy (x² + y²) is 9\(\frac { 1 }{ 9 }\).
(vi) (3x – y + 5) – (x + y) is a binomial.
(vii) Sum of 2 and p is 2p.
(viii) Sum of x² + x and y² + y is 2x² + 2y².
(ix) In like terms, variables and their powers are the same.
(x) Every polynomial is a monomial.
(xi) If we add a monomial and a binomial, then answer can never be a monomial.
(xii) If we subtract a monomial from a binomial, then the answer is at least a binomial.
(xiii) if we add a monomial and a trinomial, then the answer can be a monomial.
(xiv) If we add a monomial and a binomial, then the answer can be a trinomial.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 16):
Question 3.
The algebraic expression for the statement ‘Thrice square of a number x subtracted from five times the sum of y and 2’ is
(a) 5y + 2 – 3x²
(b) 3x² – (5y + 2)
(c) 5(y + 2) – 3x²
(d) 5(y + 2) – (3x)²
Solution:

Question 4.
The expression 7x – 5(x² + y²) is a
(a) monomial
(b) binomial
(c) trinomial
(d) none of these
Solution:

Question 5.
The coefficient of 5a² in -5a³bc is
(a) -bc
(b) a²bc
(c) -a²bc
(d) -abc
Solution:

Question 6.
Which of the following is a pair of like terms?
(a) -5xy, 5x
(b) -5xy, 3yz
(c) -5xy, -5y
(d) -5xy, 7yx
Solution:

Question 7.
The like terms is the expressions 3x(3 – 2y) and 2(xy + x²) are
(a) 9x and 2x²
(b) -6xy and 2xy
(c) 9x and 2xy
(d) -6xy and 2x²
Solution:

Question 8.
Identify the binomial out of the following:
(a) 3xy² + 5y – x²y
(b) 2x²y – 5y – 2x²y
(c) 3xy² + 5y – xy²
(d) xy + yz + zx
Solution:

Question 9.
The number of (unlike) terms in the expression 3xy² + 2y²z – y²x + y(xz + yz) – 5
(a) 3
(b) 4
(c) 5
(d) 6
Solution:

Question 10.
The value of the expression x³ + y³ when x = 2 and y = -2 is
(a) 0
(b) 8
(c) 16
(d) -16
Solution:

Question 11.
-xy – (-5xy) is equal to
(a) -6xy
(b) 6xy
(c) -4xy
(d) 4xy
Solution:

Question 12.
On subtracting 7x + 5y – 3 from 5y – 3x – 9, we get
(a) 10x + 6
(b) -10x – 6
(c) 10x + 10y – 12
(d) -10x – 12
Solution:

Question 13.
The value of the expression \(\frac { 5 }{ 3 }\) x² + 1 when x = -2 is
(a) \(\frac { -17 }{ 3 }\)
(b) \(\frac { -7 }{ 3 }\)
(c) \(\frac { 21 }{ 3 }\)
(d) \(\frac { 23 }{ 3 }\)
Solution:

Question 14.
The number of sides in a pattern having 3 hexagons arranged in a row as shown in the given figure is

(a) 18
(b) 17
(c) 16
(d) 15
Solution:

Question 15.
The degree of the polynomial 3x³y – 5xy⁴ – 2x + 1 is
(a) 5
(b) 4
(c) 3
(d) 2
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
The length of a rectangle is 3x – 4y + 6z and the perimeter is 7x + 8y + 17z, find the breadth of the rectangle.
Solution:

Question 2.

Solution:

Question 3.
If a = 3, b = -1, then find the value of each of the following:

Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Ex 8.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.4

Question 1.
Observe the patterns of shapes of letters formed from line segments of equal lengths:

If n shapes of letters are formed, then write the algebraic expression for the number of line segments required for making these n shapes in each case.
Solution:

Question 2.
Observe the pattern of shapes of digits formed from line segment of equal lengths:

If n shapes of digits are formed, then write the algebraic expression for the number of line segments required for making these n shapes in each case.
Solution:

Question 3.
If a pattern consists of n shapes formed by line segments of equal lengths and the number of line segments required to make n shapes is given by the algebraic expression:
(i) 2n + 1
(ii) 3n + 1
(iii) 3n + 2
(iv) 5n + 1
(v) 5n + 2
(vi) 4n + 3
then find the number of line segments required to form 5, 10 and 100 shapes in each case.
Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Ex 8.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.3

Question 1.
If m = 2, find the value of:
(i) 3m – 5
(ii) 9 – 5m
(iii) 3m² – 2m – 1
(iv) \(\frac { 5 }{ 2 }\) m – 4
Solution:

Question 2.
If p = – 2, find the value of:
(1) 4p + 7
(ii) -3p² + 4p + 7
(iii) -2p³ – 3p² + 4p + 7
Solution:

Question 3.
If a = 2, b = -2, find the value of:
(i) a² + b²
(ii) a² + ab + b²
(iii) a² – b²
Solution:

Question 4.
When a = 0, b = -1, find the value of the given expressions:
(i) 2a² + b² + 1
(ii) a² + ab + 2
(iii) 2a²b + 2ab² + ab
Solution:

Question 5.
If p = -10, find the value of p² – 2p – 100.
Solution:

Question 6.
If z = 10, find the value of z³ – 3(z – 10).
Solution:

Question 7.
Simplify the following expressions and find their values when x = 2:
(i) x + 7 + 4(x – 5)
(ii) 3(x + 2) + 5x – 7
(iii) 6x + 5(x – 2)
(iv) 4(2x – 1) + 3x + 11
Solution:

Question 8.
Simplify the following expressions and find their values when a = -1, b = -2:
(i) 2a – 2b – 4 – 5 + a
(ii) 2(a² + ab) + 3 – ab
Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Ex 8.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.2

Question 1.
Add:
(i) 7x, -3x
(ii) 6x, -11x
(iii) 5x², -9x²
(iv) 3ab², -5ab²
(v) \(\frac { 1 }{ 2 }\) pq, \(\frac { -1 }{ 3 }\) pq
(vi) 5x³y, \(\frac { -2 }{ 3 }\) x³y
Solution:

Question 2.
Add:
(i) 3x, -5x, 7x
(ii) 7xy, 2xy, -8xy
(iii) -2abc, 3abc, abc
(iv) 3mn, -5mn, 8mn, -4mn
(v) 2x³, 3x³, -4x³, -5x³
Solution:

Question 3.
Simplify the following combining like terms:
(i) 21b – 32 + 7b – 20b
(ii) 12m² – 9m + 5m – 4m² – 7m + 10
(iii) -z² + 13z² – 5z + 7z² – 15z
(iv) 5x²y – 5x² + 3yx² – 3y² + x² – y² + 8xy² – 3y²
(v) p – (p – q) – (q – p) – q
(vi) 3a – 2b – ab – (a – b + ab) + 3ab + b – a
(vii) (3y² + 5y – 4) – (8y – y² – 4)
Solution:

Question 4.
Find the sum of the following algebraic expressions:
(i) 5xy, -7xy, 3x²
(ii) 4x²y, -3xy², -5xy², 5x²y
(iii) -7mn + 5, 12mn + 2, 8mn – 8, -2mn – 3
(iv) a + b – 3, b – a + 3, a – b + 3
(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy
(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5
(vii) 3x³ – 5x² + 2x + 1, 3x – 2x² – x³, 2x² – 7x + 9
(viii) 7a² – 5a + 2, 3a² – 7, 2a + 9, 1 + 2a – 5a²
Solution:

Question 5.
Simplify the following:
(i) 2x² + 3y² – 5xy + 5x² – y² + 6xy – 3x²
(ii) 3xy² – 5x²y + 7xy – 8xy² – 4xy + 6x²y
(iii) 5x⁴ – 7x² + 8x – 1 + 3x³ – 9x² + 7 – 3x⁴ + 11x – 2 + 8x²
Solution:

Question 6.
Subtract:
(i) -5y² from y²
(ii) -7xy from -2xy
(iii) a(b – 5) from b(5 – a)
(iv) -m² + 5mn from 4m² – 3mn + 8
(v) 5a² – 7ab + 5b² from 3ab – 2b – 2b²
(vi) 4pq – 5q² – 3p² from 5p² + 3q² – pq
(vii) 7xy + 5x² – 7y² + 3 from 7x² – 8xy + 3y² – 5
(viii) 2x⁴ – 7x² + 5x + 3 from x⁴ – 3x³ – 2x² + 3
Solution:

Question 7.
Subtract p – 2q + r from the sum of 10p – r and 5p + 2q.
Solution:

Question 8.
From the sum of 4 + 3x and 5 – 4x + 2x², subtract the sum of 3x² – 5x and -x² + 2x + 5.
Solution:

Question 9.
What should be added to x² – y² + 2xy to obtain x² + y² + 5xy?
Solution:

Question 10.
What should be subtracted from -7mn + 2m² + 3n² to get m² + 2mn + n²?
Solution:

Question 11.
How much is y⁴ – 12y² + y + 14 greater than 17y³ + 34y² – 51y + 68?
Solution:

Question 12.
How much does 93p² – 55p + 4 exceed 13p³ – 5p² + 17p – 90?
Solution:

Question 13.
What should be taken away from 3x² – 4y² + 5xy + 20 to obtain -x² – y² + 6xy + 20?
Solution:

Question 14.
From the sum of 2y² + 3yz, -y² – yz – z² and yz + 2z², subtract the sum of 3y² – z² and -y² + yz + z².
Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Ex 8.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.1

Question 1.
From the algebraic expressions using variables, constants, and arithmetic operations:
(i) 6 more than thrice a number x.
(ii) 5 times x is subtracted from 13.
(iii) The numbers x and y both squared and added.
(iv) Number 7 is added to 3 times the product of p and q.
(v) Three times of x is subtracted from the product of x with itself.
(vi) Sum of the numbers m and n is subtracted from their product.
Solution:

Question 2.
A taxi charges ₹ 9 per km and a fixed charge of ₹ 50. If the taxi is hired for x km, write an algebraic expression for this situation.
Solution:

Question 3.
Write down the algebraic expression whose terms are:
(i) 5a, -3b, c
(ii) x², -5x, 6
(iii) x²y, xy, -xy²
Solution:

Question 4.
Write all the terms of each of the following algebraic expressions:
(i) 3 – 7x
(ii) 2 – 5a + \(\frac { 1 }{ 2 }\) b
(iii) 3x⁵ + 4y³ – 7xy² + 3
Solution:

Question 5.
Identify the terms and their factors in the algebraic expressions given below:
(i) -4x + 5y
(ii) xy + 2x²y²
(iii) 1.2ab – 2.4b + 3.6a
Solution:

Question 6.
Show the terms and their factors by tree diagrams of the following algebraic expressions:
(i) 8x + 3y²
(ii) y – y³
(iii) 5xy² + 7x²y
(iv) -ab + 2b² – 3a²
Solution:

Question 7.
Write down the numerical coefficient of each of the following:
(i) -7x
(ii) -2x³y²
(iii) 6abcd²
(iv) \(\frac { 2 }{ 3 }\) pq²
Solution:

Question 8.
Write down the coefficient of x in the following:
(i) -4bx
(ii) 5xyz
(iii) -x
(iv) -3x²y
Solution:

Question 9.
In -7xy²z³, write down the coefficient of:
(i) 7x
(ii) -xy²
(iii) xyz
(iv) 7yz²
Solution:

Question 10.
Identify the terms (other than constants) and write their numerical coefficients in each of the following algebraic expressions:
(i) 3 – 7x
(ii) 1 + 2x – 3x²
(iii) 1.2a + 0.8b
Solution:

Question 11.
Identify the terms which contain x and write the coefficient of x in each of the following expressions:
(i) 13y² – 8xy
(ii) 7x – xy²
(iii) 5 – 7xyz + 4x²y
Solution:

Question 12.
Identify the term which contain y2 and write the coefficient of y2 in each of the following expressions:
(i) 8 – xy²
(ii) 5y² + 7x – 3xy²
(iii) 2x²y – 15xy² + 7y²
Solution:

Question 13.
Classify into monomials, binomials and trinomials:
(i) 4y – 7z
(ii) -5xy²
(iii) x + y – xy
(iv) ab² – 5b -3a
(v) 4p²q – 5pq²
(vi) 2017
(vii) 1 + x + x²
(viii) 5x² – 7 + 3x + 4
Solution:

Question 14.
State whether the given pair of terms is of like or unlike terms:
(i) -7x, \(\frac { 5 }{ 2 }\) x
(ii) -29x, -29y
(iii) 2xy, 2xyz
(iv) 4m²p, 4mp²
(v) 12xz, 12x²z²
(vi) -5pq, 7qp
Solution:

Question 15.
Identify like terms in the following:
(i) x²y, 3xy², -2x²y, 4x²y²
(ii) 3a²b, 2abc, -6a²b, 4abc
(iii) 10pq, 7p, 8q – p²q², -7qp, -100q, -23, 12q²p², -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²
Solution:

Question 16.
Write down the degree of following polynomials in x:
(i) x² – 6x⁷ + x⁸
(ii) 3 – 2x
(iii) -2
(iv) 1 – x²
Solution:

Question 17.
Write the degree of the following polynomials:
(i) 3x² – 5xy² + 7
(ii) xy² – y³ + 3y⁴ – 2
(iii) 7 – 2x³ – 5xy³ + 9y⁵
Solution:

Question 18.
State true or false:
(i) If 5 is constant andy is variable, then 5y and 5 + y are variables
(ii) 7x has two terms, 7 and x
(iii) 5 + xy is a trinomial
(iv) 7a × bc is a binomial
(v) 7x³ + 2x² + 3x – 5 is a polynomial
(vi) 2x² – \(\frac { 3 }{ x }\) is a polynomial
(vii) Coefficient of x in -3xy is -3
Solution:

ML Aggarwal Class 7 Solutions Chapter 12 Congruence of Triangles Ex 12.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.2

Question 1.
You want to establish ΔDEF = ΔMNP, using ASA rule of congruence. You are given that ∠D = ∠M and ∠F = ∠P. What additional information is needed to establish the congruence?
Solution:

Question 2.
In the given figure, two triangles are congruent. The corresponding parts are marked. We can write ΔRAT =?

Solution:

Question 3.
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

Solution:

Question 4.
Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by ASA congruence rule. In the case of congruence, write its in symbolic form.

Solution:

Question 5.
In the adjoining figure, measures of some parts are indicated.
(i) State three pairs of equal parts in triangles ABC and ABD.
(ii) Is ΔABC = ΔBAD? Give reasons.
(iii) Is BC = AD? Why?

Solution:

Question 6.
In the adjoining figure, ray AZ bisects ∠DAB as well as ∠DCB.
(i) State the three pairs of equal parts in triangles BAC and DAC.
(ii) Is ΔBAC = ΔDAC? Give reasons.
(iii) Is CD = CB? Give reasons.

Solution:

Question 7.
Explain why ΔABC = ΔFED?

Solution:

Question 8.
Given below are the measurements of some parts of triangles. Examine whether the two triangles are congruent or not, using RHS congruence rule. In the case of congruent triangles, write the result in symbolic form

Solution:

Question 9.
In the given figure, measurements of some parts are given.
(i) State the three pairs of equal parts in ΔPQS and ΔPRS.
(ii) Is ΔPQS = ΔPRS? Give reasons.
(iii) Is S mid-point of \(\bar { QR }\) ? Why?

Solution:

Question 10.
In the given figure, O is mid-point of \(\bar { AB }\) and ∠A = ∠B. Show that ΔAOC = ΔBOD.

Solution:

ML Aggarwal Class 7 Solutions Chapter 12 Congruence of Triangles Ex 12.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 12 Congruence of Triangles Ex 12.1

Question 1.
If ΔABC and ΔDEF are congruent under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.
Solution:

Question 2.
If ΔDEF = ΔBCA, then write the part(s) of ΔBCA that correspond to
(i) ∠E
(ii) \(\bar { EF }\)
(iii) ∠F
(iv) \(\bar { DF }\)
Solution:

Question 3.
In the figure given below, the lengths of the sides of the triangles are indicated. By using SSS congruency rule, state which pairs of triangles are congruent. In the case of congruent triangles, write the result in symbolic form:

Solution:

Question 4.
In the given figure, AB = 5 cm, AC = 5 cm, BD = 2.5 cm and CD = 2.5 cm
(i) State the three pairs of equal parts in ΔADB and ΔADC
(ii) Is ΔADB = ΔADC? Give reasons.
(iii) Is ∠B = ∠C? Why?

Solution:

Question 5.
In the given figure, AB = AC and D is the mid-point of \(\bar { BC }\).
(i) State the three pairs of equal parts in ΔADB and ΔADC.
(ii) Is ΔADB = ΔADC? Give reasons.
(iii) Is ∠B = ∠C? Why?

Solution:

Question 6.
In the figure given below, the measures of some parts of the triangles are indicated. By using SAS rule of congruency, state which pairs of triangles are congruent. In the case of congruent triangles, write the result in symbolic form.

Solution:

Question 7.
By applying SAS congruence rule, you want to establish that ΔPQR = ΔFED. If is given that PQ = EF and RP = DF. What additional information is needed to establish the congruence?
Solution:

Question 8.
You want to show that ΔART = ΔPEN

(a) If you have to use SSS criterion, then you need to show
(i) AR = ……….
(ii) RT = ……….
(iii) AT = …………
(b) If it is given that ∠T = ∠N and you are to use the SAS criterion, you need to have
(i) RT = ………. and (ii) PN = ……….
Solution:

Question 9.
You have to show that ΔAMP = ΔAMQ.
In the following proof, supply the missing reasons.

Solution:

Question 10.Solution:
In the given figure:
(i) State three pairs of equal parts in ΔPSR and ΔRQP.
(ii) Is ΔPSR = ΔRQP? Give reasons
(iii) Is PS = RQ? Why?
(iv) Is ∠S = ∠Q? Why?

Solution:

Question 11.
In the given figure, AB = DC and ∠ABC = ∠DCB.
(i) State three pairs of equal parts in AABC and ADCB.
(ii) Is ΔABC = ΔDCB? Give reasons.
(iii) Is AC = DB? Why?

Solution:

Question 12.
In the quadrilateral, AC = AD, and AB bisect ∠CAD.
(i) State three pairs of equal parts in ΔABC and ΔABD.
(ii) Is ΔABC = ΔABD? Give reasons.
(iii) Is BC = BD? Why?
(iv) Is ∠C = ∠D? Why?

Solution: