NCERT Class 9th solution of Exercise 6.1 NCERT Class 9th solution of Exercise 6.2 Exercise 6.3 Q1. In the given figure, sides `QP` and `RQ` of `△PQR` are produced to points `S` and `T` respectively. If `∠SPR=135°` and `∠PQT=110°`, find `∠PRQ`. Sol. `∠PQT+∠PQR=180°`  [ By linear pair. ] `110°+∠PQR=180°`    [ Given `∠PQT=110°` ] `∠PQR=180°-110°` `∠PQR=70°` `∠PRQ+∠PQR=∠SPR`                               [ By exterior angle property ] `∠PRQ+70°=135°`       [ Given `∠SPR=135°` ] `∠PRQ=135°-70°` `∠PRQ=65°` Answer : The required value of `∠PRQ=65°`. Q2. In the given figure, `∠X=62°, ∠XYZ=54°`. If `YO` and `ZO` are the bisectors of `∠XYZ` and `∠XZY` respectively of `△XYZ`, find `∠OZY` and `∠YOZ`. Sol. : In `△XYZ`, `∠YXZ+∠XYZ+∠XZY=180°`                                            [ By Angle sum property of `△`] `62°+54°+∠XZY=180°` `∠XZY=180°-62°-54°` `∠XZY=180°-116°` `∠XZY=64°` `∠XZO=∠OZY=frac(1)(2)times∠XZY`                                                        [ `ZO` is bisect `∠XZY`] `∠XZO=∠

NCERT Class 9th solution of Exercise 6.1 NCERT Class 9th solution of Exercise 6.3 NCERT Class 9th Maths Projects Exercise 6.2 Q1. In the given figure, find the values of `x` and `y` and then show that `AB∥CD`. Sol. : According to the given figure `x+50=180°`        [ By linear pair ] `x=180-50°` `x=130°`____(1) `y=130°`____(2)   [ Vertically opp. angles ] `x=y=130°`           [ By eq. (1) & (2) ] `AB∥CD`.             [ Alternate angles are equal ] Proved. Q2. In the given figure, if `AB∥CD, CD∥EF` and `y:z=3:7`,find `x`. Sol. : Let ST is transversal line intersects `AB, CD,` & `EF` at `P, Q,` & `R` respectively,  According to the given figure `∠DQR=∠PQC=y` [ Vertically opp. angles and given `∠PQC=y`] `∠DQR=y` `∠DQR+∠QRF=180°` [ linear pair and given `∠QRF=z` ] `y+z=180°`             [ Sum of  interior angles on the same side ] The Sum of the ratio of `y` & `z` is `3+7=10` `y=frac(3)(10)times180°` `y=54°` `z=frac(7)(10)times180°` `x=z=126°` [Alternate angles are equal] A

NCERT Class 9th solution of Exercise 6.2 NCERT Class 9th solution of Exercise 6.3 NCERT Class 9th solution of Exercise 5.1 NCERT Class 9th Maths Projects Exercise 6.1 Q1. In the given figure lines `AB` and `CD` intersect at `O`, if `∠AOC + ∠BOE = 70°` and `∠BOD = 40°` then find the `∠BOE` and reflex `∠COE`. Sol. `∠AOC=∠BOD`_______(1) [Vertically opp. angles] `∠AOC=40°`    ________(2) [ Given `∠BOD=40°`] `∠AOC+∠BOE=70°`____(3) [Given] `40°+∠BOE=70°`                    [ from eq. (2) ] `∠BOE=70°-40°` `∠BOE=30°`__________(4) Now `∠AOC+∠COE+∠BOE=180°`   [ By Linear pair] `40°+∠COE+30°=180°`           [ from eq. (2) & (4) ]          `∠COE=180°-70°` `∠COE=110°` Reflex`∠COE=360°-∠COE` Reflex`∠COE=360°-110°` Reflex`∠COE=250°` Answer : The required `∠BOE=30°` and reflex`∠COE=250°`. Q2. In the figure lines, `XY` and `MN` intersect at `O`. If `∠POY=90°` and `a:b=2:3`, find `c`. Sol. `∠XOP+∠POY=180°`    [ By linear pair ] `(∠XOM+∠MOP)+90°=180°` [ Given `∠POY=90°`] `(a+b)=180°-90°` `a+b=90°` Su

NCERT Class 9th solution of Exercise 5.1 NCERT Class 9th solution of Exercise 6.1 NCERT Class 9th Maths Projects Exercise 5.2 Q1. How would you rewrite Euclid's fifth postulate so that it would be easier to understand? Answer : If a straight line intersects two other straight lines and the sum of the two interior angles formed on the same side is less than two right angles (180°) then the two-line are intersecting lines. Q2. Does Euclid's fifth postulate imply the existence of parallel lines? Explain. Answer : If a straight line `l` falls on two straight lines `m` and `n` such that sum of the interior angles on one side of `l` is two right angles, then by Euclid's fifth postulate the line will not meet on this side of `l`. Next, you know that the sum of the interior angles on the other side of line `l` will also be two right angles. Therefore, they will not meet on the other side also. So, the lines `m` and `n` never meet and are, therefore, parallel.

NCERT Class 9th solution of Exercise 5.2 NCERT Class 9th solution of Exercise 4.1 NCERT Class 9th Maths Projects Exercise 5.1  Q1. Which of the following statements are True and which are False? Give reason for your answers : i)  Only one line can pass through a single point. ii) There are an infinite number of lines which pass through two different points. iii) A terminated line can be produced infinitely on both the sides. iv) If two circles are equal, then their radius are equal. v) In the following figure if `AB=PQ` and `PQ=XY`, then `AB=XY`. Answer : i) False. Infinitely many lines can pass through a single. ii) False. One and only one line can pass through two different points. iii) True. A terminated line can be produced indefinitely. iv) True. If you superimpose the bounded by one circle on the other, then they coincide. So, their certres and boundaries coincide. Therefore, their radii will coincide. v) True. Things which are equal to the same things are equal to one another. Q

NCERT Class 9th solution of Exercise 4.1 NCERT Class 9th solution of Exercise 4.2 NCERT Class 9th solution of Exercise 4.3 NCERT Class 9th Maths Projects Exercise 4.4 Q1. Give the geometric representation of  `y=3` as an equation : i) in one variable,  ii) in two variables. Sol. : i) in one variable, Geometric representation of `y=3` as an equation in one variable : ii) in two variables. Geometric representation of `y=3` as an equation in two variables :   Q2. Give the geometric representations of `2x+9=0` as an equation : i) in one variable,  ii) in two variables. Sol. : i) in one variable Geometric representation of `2n+9=0` as an equation in one variable ii) in two variables Geometric representation of `2n+9=0` as an equation in two variables

NCERT Class 9th solution of Exercise 4.1 NCERT Class 9th solution of Exercise 4.2 NCERT Class 9th solution of Exercise 4.4 NCERT Class 9th Maths Projects Exercise 4.3 Q1. Draw the graph of each of the following linear equations in two variables : i) `x+y=4` ii) `x-y=2` iii) `y=3x` iv) `3=2x+y` Sol. : i) Given equation `x+y=4` then `y=4-x` When `x=0` `y=4-0` `y=4` when `x=1` `y=4-1` `y=3` when `y=0` `0=4-x` `x=4` X 0 1 4 y 4 3 0 ii) Given equation `x-y=2` then `y=x-2` when `x=0` `y=0-2` `y=-2` when `x=1` `y=1-2` `y=-1` when `y=0` `0=x-2` `x=2` X 0 1 2 y -2 -1 0 iii) Given equation `y=3x` When `x=0` `y=3(0)` `y=0` when `x=1` `y=3(1)` `y=3` when `x=-1` `y=3(-3)` `y=-3` X 0 1 -1 y 0 3 -3 iv) Given equation `3=2x+y` then `y=3-2x` when `x=0` `y=3-2(0)`