SChand Composite Mathematics Class 7 Chapter 13 Congruence of Triangle Exercise 13C

 Exercise 13 C 

Question 1 

(a) What will be the other angles of a right angles isosceles triangle? 

Sol: $x+x+90=180^{\circ} \Rightarrow 2x=90 \Rightarrow x=45^{\circ} \quad 45^{\circ}$

(b) Can you draw an obtuse angles isosceles triangle ? 

Ans: Yes

Question 2

(a) The vertical angle of an isosceles triangle is 110 degree. What must be the size of its base angles? 

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Sol: $\Rightarrow \quad x+x+110^{\circ}=180^{\circ}$

$\Rightarrow \quad 2 x=180^{\circ}-110^{\circ} \Rightarrow \quad 2 x=70^{\circ}$

x = $35^{\circ}$  Ans

(b) What is the size of each exterior angle of an equilateral triangle ? 

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Sol: $180^{\circ}-60^{\circ}=x$

$x=120^{\circ}$

Question 3

$\triangle A B C$ is isosceles with AB= AC, if $\angle A=80^{\circ}$ what is the measure of angle b?

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Sol: Let $\angle B=\angle C=x$

$\Rightarrow x+x+80^{\circ}=180^{\circ}$

$\Rightarrow 2 x=180^{\circ}-80^{\circ}$

$\Rightarrow 2 x=100^{\circ}$

$\Rightarrow  x=50^{\circ}$

$\angle B=\angle L=50^{\circ}$

Question 4

In $\triangle B B C, \angle A=\angle B=50^{\circ}$. Name the pair of sides which are equal . 

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Side AC = BC 

Question 5

In the figure given below AN =AC, $\angle B A C=52^{\circ}$ $\angle A C K=84^{\circ}$ and BCK is  a straight line . prove that NB =NC

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Sol: $\triangle A B C$

$\angle A+\angle B=84^{\circ}$

$52^{\circ}+\angle B=84^{\circ}$

$\begin{aligned} \angle B &=84^{\circ}-52^{\circ} \\ \Rightarrow \angle B &=32^{\circ} \end{aligned}$

$\triangle A N C$

$\Rightarrow \quad 52^{\circ}+x+x=180^{\circ}$

$\Rightarrow \quad 2 x=180^{\circ}-52^{\circ}$ $2x=123^{\circ}$

$\Rightarrow x=\frac{128}{2} \quad \Rightarrow$

x = $64^{\circ}$

∵ BCK Straight line 

$\angle B C N+\angle A C N+\angle A C K=180^{\circ}$

$\angle B C N+64^{\circ}+84^{\circ}=180^{\circ}$

$\angle B C N=180^{\circ}-148$

$\angle B C N=32^{\circ}$

$\because \angle B C N=\angle B$

BN = NC Hence proved 

Question 6

In the figure AB = AC. Prove that BD = BC

Sol: $\Rightarrow x+x+40^{\circ}=180$

$\Rightarrow 2 x=180^{\circ}-40^{\circ}$

$\Rightarrow 2 x=140^{\circ}$

$\Rightarrow x=\frac{140^{\circ}}{2}$

$\Rightarrow x=70^{\circ}$

By ext. angle prop

$\Rightarrow 30^{\circ}+40^{\circ}=y$

$\Rightarrow y=70^{\circ}$

$\because x=y=70^{\circ}$

$\therefore B D=B C$ Hence proved 

S.chand class 6 Mathematics Chapter 13 Exercise 13C

 Exercise 13C

Question 1

1. Classify as constants or variables: $4,-8 y, \frac{3}{7},-8,9 x, a b, \frac{b x}{y}, 0, \frac{3 x^{2}}{2 z}$.

2. Write all the terms of the following algebraic expressions.

(i) $3 x+5 y-6 z$

(ii) $6 a^{2}+5 b^{2}-3 c d$

(iii) $7-9 x^{2}+5 y$

(iv) $4 a^{2}-7 b^{2}+2 a b-1$

3. Write down the algebraic expression whose terms are

(i) $4 a^{2},-2 b^{2},-3$

(ii) $7 x,-5,8 x^{2}$

(iii) $-3 p^{2}, 2 q^{2},-6 p q,-5$

(iv) $\frac{2}{3} x^{2},-\frac{4}{7} x y, 3 y^{2}$

4. Identify monomials, binomials and trinomials from the following.

(i) $2 m+3 n$

(ii) $a-5 b+7 c$

(iii) $\frac{2}{7} a^{2}$

(iv) $5 m^{2}-4$

(v) $7 a^{2}+2 b^{2}-4 a b$

(vi) $\frac{1}{2} x^{3}-y+z$

5. Write the coefficient of "a" in the following.

(i) $3 a$

(ii) pa

(iii) $-3 p a$

(iv) $4 a y^{2}$

(v) $-\frac{1}{5} a p$

6. Write the coefficient of

(i) $x$ in $-7 x y^{2}$

(ii) $m$ in $m x^{2}$

(iii) $x^{2} y$ in $\frac{5}{9} a x^{2} y$

(iv) $a$ in - $a$

7. Write down the numerical as well as the literal coefficient of the following monomials.

(i) $-12 x^{2} y$

(ii) $\frac{8}{15} a^{2} b c$

(iii) $-\frac{7}{9} a b c$

(iv) $-2 p q$

(v) $\frac{-3 x y}{7 z}$

(vi) $-6 x^{2} y^{2} z^{2}$

8. Identify the like terms in the following.

(i) $x^{2}, y^{2}, 2 x^{2}, z^{2}$

(ii) $3 x y, y z, 5 x, \frac{2}{7} y z$

(iii) $c a b^{2}, a^{2} b c, b^{2} a c, c^{2} a b, a b c, a c b^{2}$

9. Rearrange the factors so that literal factors are arranged alphabetically and follow the numerical factors.

(i) p3 q2r4s

(ii) $d e f 15 c$

(iii) $x 4 y z 2$

(iv) $5 w 2 t$

10. Which of the following algebraic expressions are polynomials?

(i) $x^{2}-\frac{1}{x^{2}}+2$

(ii) $\frac{3}{7} x^{2}-\frac{3}{7} x^{2}+3$

(iii) $81 x^{2}+4 x y-9 y^{2}-6$

(iv) $\frac{2}{x}+\frac{3}{x^{2}}-4 x^{2}-2 x+3$

(v) $8 x^{3}+7 x^{2}-12 x+4$

(vi) $p^{2}+p^{2} q-\frac{4 p}{q}+8$

11. Write down the degrees of the following polynomials.

(i) $a b+b c+c a$

(ii) $2+p^{2}$

(iii) $3 x^{2}-x^{4}$

(iv) $3 p^{2}+5 p^{3}+7 p^{5}$

(v) 4

(vi) $2 x^{2}+x y z+3 y^{3}$

(vii) $a^{2} b+a^{3} b^{2}+2 a b$

Multiple Choice Question (MCQ)

Tick (✔) the correct option.

12. A constant is a polynomial of degree

(a) 1

(b) 0

(c) cannot be determined

(d) None of these