# NCERT Solutions for Class 7 Maths Ch 10 Practical Geometry

**Chapter 10 Practical Geometry Class 7 Maths NCERT Solutions**is provided here that will help you in finding the accurate and detailed answers of every questions given in the chapter, Whenever you'll be in doubt or finding difficulty while solving a specific question you can take help from the given NCERT Solutions for Class 7. These NCERT Solutions will be helpful in knowing the important points inside the chapter.

**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.

**Answer**

To construct: A line, parallel to given line by using ruler and compasses.

Steps of construction:

(a) Draw a line-segment AB and take a point C outside AB.

(b) Take any point D on AB and join C to D.

(c) With D as centre and take convenient radius, draw an arc cutting AB at E and CD at F.

(d) With C as centre and same radius as in step 3, draw an arc GH cutting CD at I.

(e) With the same arc EF, draw the equal arc cutting GH at J.

(f) Join JC to draw a line l. This the required 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.

**Answer**

To construct: A line parallel to given line when perpendicular line is also given.

Steps of construction:

(a) Draw a line l and take a point P on it.

(b) At point P, draw a perpendicular line n.

(c) Take PX = 4 cm on line n.

(d) At point X, again draw a perpendicular line m.

Given figure is the required construction.

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?

**Answer**

To construct: A pair of parallel lines intersecting other part of parallel lines.

Steps of construction:

(a) Draw a line l and take a point P outside of l .

(b) Take point Q on line l and join PQ.

(c) Make equal angle at point P such that âˆ Q = âˆ P.

(d) Extend line at P to get line m.

(e) Similarly, take a point R online m, at point R, draw angles such that âˆ P = âˆ R.

(f) Extended line at R which intersects at S online l. Draw line RS.

Thus, we get parallelogram PQRS.

**Exercise 10.2**

1. Construct Î”XYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.

**Answer**

To construct: Î”XYZ, where XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.

Steps of construction:

(a) Draw a line segment YZ = 5 cm.

(b) Taking Z as centre and radius 6 cm, draw an arc.

(c) Similarly, taking Y as centre and radius 4.5 cm, draw another arc which intersects first arc at point X.

(d) Join XY and XZ. It is the required Î”XYZ.

2. Construct an equilateral triangle of side 5.5 cm.

**Answer**

To construct: A Î”ABC where AB = BC = CA = 5.5 cm

Steps of construction:

(a) Draw a line segment BC = 5.5 cm

(b) Taking points B and C as centers and radius 5.5 cm, draw arcs which intersect at point A.

(c) Join AB and AC. It is the required Î”ABC.

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

**Answer**

To construction: Î”PQR, in which PQ = 4 cm, QR = 3.5 cm and PR = 4 cm.

Steps of construction:

(a) Draw a line segment QR = 3.5 cm.

(b) Taking Q as centre and radius 4 cm, draw an arc.

(c) Similarly, taking R as centre and radius 4 cm, draw an another arc which intersects first arc at P.

(d) Join PQ and PR. It is the required isosceles Î”PQR.

**Answer**

To construct: Î”ABC in which AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm.

Steps of construction:

(a) Draw a line segment BC = 6 cm.

(b) Taking B as centre and radius 2.5 cm, draw an arc.

(c) Similarly, taking C as centre and radius 6.5 cm, draw another arc which intersects first arc at point A.

(d) Join AB and AC.

(e) Measure angle B with the help of protractor. It is the required Î”ABC where âˆ B = 80Â°.

**Exercise 10.3**

1. Construct Î”DEF such that DE = 5 cm, DF = 3 cm and âˆ EDF = 90Â°.

**Answer**

To construct: Î”DEF where DE = 5 cm, DF = 3 cm and m âˆ EDF = 90Â°.

Steps of construction:

(a) Draw a line segment DF = 3 cm.

(b) At point D, draw an angle of 90o with the help of compass i.e., âˆ XDF = 90Â°.

(c) Taking D as centre, draw an arc of radius 5 cm, which cuts DX at the point E.

(d) Join EF. It is the required right angled triangle DEF.

2. Construct an isosceles triangle in which the lengths of each of its equal sides is 6.5 cm and the angle between them is 110Â°.

**Answer**

To construct: An isosceles triangle PQR where PQ = RQ = 6.5 cm and âˆ Q = 110Â°

Steps of construction:

(a) Draw a line segment QR = 6.5 cm.

(b) At point Q, draw an angle of 110Â° with the help of protractor, i.e., âˆ YQR = 110Â°

(c) Taking Q as centre, draw an arc with radius 6.5 cm, which cuts QY at point P.

(d) Join PR

Given figure is the required isosceles triangle PQR.

3. Construct Î”ABC with BC = 7.5 cm, AC = 5 cm and m âˆ C = 60Â° .

**Answer**

To construct: Î”ABC where BC = 7.5 cm, AC = 5 cm and m âˆ C = 60Â°.

Steps of construction:

(a) Draw a line segment BC = 7.5 cm.

(b) At point C, draw an angle of 60 with the help of protractor, i.e., âˆ XCB = 60Â° .

(c) Taking C as centre and radius 5 cm, draw an arc, which cuts XC at the point A.

(d) Join AB It is the required triangle ABC.

**Exercise 10.4**

1. Construct Î”ABC, given mâˆ A = 60Â°, mâˆ B = 30Â° and AB = 5,8 cm.

**Answer**

To construct: Î”ABC, given mâˆ A = 60Â°, mâˆ B = 30Â° and AB = 5,8 cm.

Steps of construction:

(a) Draw a line segment AB = 5.8 cm.

(b) At point A, draw an angle Z YAB = 60Â°= with the help of a compass.

(c) At point B, draw Z XBA = 30Â° with the help of a compass.

(d) AY and BX intersect at the point C.

Given figure is the required triangle ABC.

2. Construct Î” PQR if PQ = 5 cm, mâˆ PQR = 105Â° and mâˆ .QRP = 40Â°.

**Answer**

Given:

mâˆ PQR = 105Â° and mâˆ QRP = 40Â°

We know that sum of angles of a triangle is 180Â°.

âˆ´ mâˆ PQR + mâˆ QRP + mâˆ QPR = 180Â°

â‡’ 105Â° + 40Â° + mâˆ QPR= 180Â°

â‡’ 145Â° + mâˆ QPR= 180Â°

â‡’ mâˆ QPR= 180Â° - 145Â°

â‡’ mâˆ QPR = 35Â°

To construct: Î”PQR where mâˆ P = 35Â°, mâˆ Q = 105Â° and PQ = 5 cm.

Steps of construction:

(a) Draw a line segment PQ = 5 cm,

(b) At point P, draw âˆ XPQ = 35Â° with the help of protractor.

(c) At point Q, draw âˆ YQP = 105Â° with the help of protractor.

(d) XP and YQ intersect at point R.

It is the required triangle PQR.

3. Examine whether you can construct Î”DEF such that EF = 7.2 cm, mâˆ E= 110Â° and mâˆ F= 80Â°. Justify your answer.

**Answer**

Given: In Î”DEF, mâˆ E = 110Â° and mâˆ T = 80Â°

Using angle sum property of triangle

âˆ D + âˆ E + âˆ F = 180Â°

â‡’âˆ D + 110Â°+ 80Â° = 180Â°

â‡’ âˆ D + 190Â° = 180Â°

â‡’ âˆ D = 180Â° - 190Â° = -10Â°

Which is not possible.

**Exercise 10.5**

1. A right angled triangle PQR where mâˆ Q = 9ff, QR= 8 cm and PQ = 10 cm.

**Answer**

To construct: Construct the right angled Î” PQR, where mâˆ Q = 90", QR = 8 cm and PR = 10 cm.

Steps of construction:

(a) Draw a line segment QR = 8 cm,

(b) At point Q, draw QX âŠ¥ QR,

(c) Taking R as centre, draw an arc of radius 10 cm.

(d) This arc cuts QX at point P.

(e) foin PQ.

Given figure is the required right-angled triangle PQR,

2. Construct a right-angled triangle whose hypotenuse is 6 cm long and one the legs is 4 cm long.

**Answer**

To construct: A right-angled triangle DEF where DF = 6 cm and EF = 4 cm.

Steps of construction:

(a) Draw a line segment EF = 4 cm.

(b) At point Q, draw EX âŠ¥ EF.

(c) Taking F as centre and radius 6 cm, draw an arc. (Hypotenuse)

(d) This arc cuts the EX at point D.

(e) Join DF.

It is the required right-angled triangle DEF.

3. Construct an isosceles right angled triangle ABC, where mâˆ ACB = 90Â° and AC = 6 cm.

**Answer**

To construct: An isosceles right angled triangle ABC where mâˆ C = 90% AC = BC = 6 cm.

Steps of construction:

(a) Draw a line segment AC = 6 cm.

(b) At point C, draw XC âŠ¥ CA.

(c) Taking C as centre and radius 6 cm, draw an arc.

(d) This arc cuts CX at point B.

(e) Join BA.

It is the required isosceles right-angled triangle ABC.