*NCERT Solutions of Chapter: Practical Geometry. NCERT Solutions along with worksheets and notes for Class 7.*

**Exercise 10.1**

**(1) Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.**

**Ans-**

**Construction:-**

**(i)**Draw a line AB. Take a point C outside it and take a point P on it.

**(ii)**Join point C to point P, with P as centre and a convenient radius; draw an arc cutting AB at D and PC at E.

**(iii)**Now with same radius and C as centre, draw an arc FG cutting PC at H.

**(iv)**Place the tip of the compasses at D and adjust the opening so that the pencil tip is at E.

It does not need any drawings.

**(v)**With the same opening and with H as centre, draw an arc cutting the arc FG at I.

**(vi) **Join C and I to draw a parallel line.

**(2) Draw a line l. Draw a perpendicular to l at any point on l. On this Perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.**

**Ans-**

**Construction:-**

**(i)**Draw a line l. Take two points P and Q on it.

**(ii)** Take P as centre and a radius of more than half of PQ. Draw an arc upside the line l.

**(iii) **Now, with same radius and Q as center draw an arc upside the line l, cutting previous arc at R.

**(iv)**Join R to line l at S. RS is a perpendicular to line l.

**(v)**Take point X on RS at 4 cm away from line l. Take another point Y on PQ.

**(vi)**Join X and Y.

**(vii)** With Y as center and a convenient radius, draw an arc cutting XY at F and PQ at E.

**(viii)** With X as center and the same radius, draw an arc AB, cutting RS at C.

**(ix)**Place the pointed tip of the compasses at E and adjust the opening so that the pencil tip is at F.

It does not need drawing.

**(x)**With the same opening and with C as enter, draw an arc cutting the arc AB at D.

**(xi)** Now, join D and X to draw a line m.

**(3)** **Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose?**

**Ans-**

**(i) **Draw a line l. Take a point P outside it. Take a point T on line l. Join P and T.

**(ii) **With T as center and a convenient radius, draw an arc cutting PT at A and Line l at B.

**(iii) **Now with P as center and the same radius, draw an arc CD cutting PT at E.

**(iv)** Place the pointed tip of the compasses at B and adjust the opening so that the pencil tip is at A.

It does not need drawing.

**(v) **With the same opening and E as center, draw an arc cutting the arc CD at Z.

**(vi) **Now join P and Z to draw a line m.

**(vii) **Take a point R on line m. Join P to a point Q on line l. With P as center and a convenient radius, draw an arc cutting PQ at G and line m at F.

**(viii) **Now with R as center and the same radius, draw an arc HI.

**(ix) **Place the pointed tip of the compasses at G and adjust the opening so that the pencil tip is at F.

It does not need any drawing.

**(x) **With the same opening and R as center, draw an arc cutting the arc HI at J.

**(xi) **Now join R and J to draw a line RS.

QPRS is a quadrilateral.

**Exercise 10.2**

**(1) Construct ΔXYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.**

**Ans-**

**Construction of ΔXYZ- **

**(i) **Draw a line XY.

**(ii) **With center X, draw an arc of 4.5 cm.

**(iii) **With center Y, draw an arc of 6 cm.

**(iv) **Mark the point of intersection of arcs as Z. Join ZY and ZX. XYZ is required triangle.

**(2) Construct an equilateral triangle of side 5.5 cm.**

**Ans-**

Construction of ΔXYZ

**(i) **Draw a line XY=5.5cm.

**(ii) **With center X, draw an arc of 5.5 cm.

**(iii) **With center Y, draw an arc of 5.5 cm.

**(iv) **Mark the point of intersection of arcs as Z. Join ZY and ZX. XYZ is required triangle.

**(3)Draw PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?**

**Ans-**

Construction of ΔPQR

**(i) **Draw a line QR=3.5 cm.

**(ii) **With center Q, draw an arc of 4 cm.

**(iii) **With center R, draw an arc of 4 cm.

**(iv) **Mark the point of intersection of arcs as P. Join PQ and PR.

PQR is required isosceles triangle.

**(4) Construct ABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.**

**Ans-**

Construction of ΔABC

**(i)**Draw a line BC=6 cm.

**(ii) **With center B, draw an arc of 2 cm.

**(iii) **With center C, draw an arc of 6.5 cm.

**(iv)**Mark the point of intersection of arcs as A. Join AB and AC.

ΔABC is required right angle triangle. So, B = 90^{0}

**Exercise 10.3**

**(1)Construct ΔDEF such that DE = 5 cm, DF = 3 cm and m ∠EDF = 90 ^{0}.**

**Ans-**

**Construction-**

**(i)**Draw a line segment DE of length 5 cm.

**(ii)** At D, draw DX making 90^{0} with DE.

**(iii) **With D as center, draw an arc of radius 3 cm. It cuts DX at the point F.

**(iv) **Join EF, ΔDEF is now obtained.

**(2) Construct an isosceles triangle in which the lengths of each of its equal sides are 6.5 cm and the angle between them is 110 ^{0}.**

**Construction-**

**(i) **Draw a line segment DE of length 6.5 cm.

**(ii) **At D, draw DX making 110^{0} with DE.

**(iii) **With D as center, draw an arc of radius 6.5 cm. It cuts DX at the point F.

**(iv) **Join EF, ΔDEF is now obtained.

**(3) Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m ∠C = 60 ^{0}**

**Ans-**

**Construction-**

**(i)**Draw a line segment BC of length 7.5 cm.

**(ii) **At C, draw CX making 60^{0} with BC.

**(iii) **With C as center, draw an arc of radius 5 cm. It cuts CX at the point A.

**(iv) **Join AB, ΔABC is now obtained.

**Exercise 10.4**

**(1) Construct ΔABC, given m ∠A = 60 ^{0}, m ∠B = 30^{0} and AB = 5.8 cm**

**Ans-**

**Construction-**

**(i) **Draw AB of length 5.8 cm.

**(ii) **At point A, draw a ray XA making an angle of 60^{0} with line AB.

**(iii) **At point B, draw a ray BY making an angle of 30^{0} with line AB.

**(iv) **C has to lie on both the rays XA and YB. So, the point of intersection of the two rays is C.

ΔABC is required triangle.

**(2) Construct ΔPQR if PQ = 5 cm, m ∠PQR = 105 ^{0} and m ∠QRP = 40^{0}**

**Ans-**

**Construction-**

**(i)**Draw PQ of length 5 cm.

**(ii)**

At point P, draw a ray XP.

∠PQR+ ∠QRP + ∠QPR = 180^{0}

105^{0}+ 40^{0} + ∠QPR = 180^{0}

∠QPR = 180^{0} – 145^{0}

∠QPR = 35^{0}

Therefore, make an angle of 35^{0} with line PQ.

**(iii) **At point Q, draw a ray YQ making an angle of 105^{0} with line PQ.

**(iv) **R has to lie on both the rays XP and YQ. So, the point of intersection of the two rays is R.

ΔPQR is required triangle.

**Exercise 10.5**

**(1)Construct the right angled ΔPQR, where m ∠Q = 90 ^{0}, QR = 8 cm and PR = 10 cm.**

**Ans-**

**Construction-**

**(i) **Draw QR of length 8 cm.

**(ii) **At Q draw QX ⊥ QR.

**(iii) **With R as center, draw an arc of radius 10 cm.

**(iv) **P has to be on the perpendicular line QX as well as on the arc drawn with centre R.

Therefore, P is the meeting point of these two.

ΔPQR is now obtained.

**(2)Construct right angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.**

**Ans-**

**Construction-**

**(i) **Draw QR of length 4 cm.

**(ii) **At Q draw QX ⊥ QR.

**(iii) **With R as center, draw an arc of radius 6 cm.

**(iv) **P has to be on the perpendicular line QX as well as on the arc drawn with centre R.

Therefore, P is the meeting point of these two.

ΔPQR is now obtained.

**(3)Construct an isosceles right angled triangle ABC, where m ∠ACB = 90 ^{0} and AC = 6 cm.**

**Ans-**

**Construction-**

**(i) **Draw AC of length 6 cm.

**(ii) **At C draw CX ⊥ AC.

**(iii) **With C as center, draw an arc of radius 6 cm. The arc will cut CX at point B.

**(iv) **B has to be on the perpendicular line CX as well as on the arc drawn with centre A.

Therefore, B is the meeting point of these two.

ΔABC is now obtained.

**Helping Topics**