NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry download the pdf given below. The foremost objective is to help students understand and crack these problems. We at BYJUâ€™S have prepared the NCERT Solutions for Class 7 Maths wherein problems are solved step by step with complete descriptions.

There are 5 exercises present in Chapter 10 â€“ Practical Geometry of NCERT Solutions for Class 7 Maths. The concepts covered in this chapter include:

- Construction of a Line Parallel To a Given Line, Through a Point Not on The Line
- Construction of Triangle
- Constructing a Triangle When the Lengths of its Three Sides are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides And The Measure of The Angle Between Them Are Known (SAS Criterion)
- Constructing a Triangle When The Measures of Two of Its Angles and The Length of The Side Inclined Between Them Is Given (ASA Criterion)
- Constructing a Right-Angled Triangle When The Length of One Leg and Its Hypotenuse are Given (RHS Criterion)

## Download the PDF of NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

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### Access Exercises of NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

### Access Answers to NCERT Class 7 Maths Chapter 10 â€“ Practical Geometry

Exercise 10.1 Page: 196

**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.**

**Solution:-**

Steps for construction

1. Draw a line AB.

2. Take any point Q on AB and a point P outside AB and join PQ.

3. With Q as center and any radius draw an arc to cut AB at E and PQ at F.

4. With P as center and same radius draw an arc IJ to cut QP at G.

5. Place the pointed tip of the compass at E and adjust the opening so that the pencil tip is at F.

6. With the same opening as in step 5 and with G as center, draw an arc cutting the arc IJ at H.

7. Now, join PH to draw a line CD.

**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.**

**Solution:-**

Steps for construction

1. Draw a line L.

2. Take any point P on line L.

3. At point P, draw a perpendicular line N.

4. Place the pointed tip of the compass at P and adjust the compass up to length of 4 cm, draw an arc to cut this perpendicular at point X.

5. At point X, again draw a perpendicular 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?**

**Solution:-**

Steps for construction

1. Draw a line L.

2. Take any point Q on L and a point P outside L and join PQ.

3. Make sure that angles at point P and point Q are equal i.e. âˆ Q = âˆ P

4. At point P extend line to get line M which is parallel L.

5. Then take any point R on line M.

6. At point R draw angle such that âˆ P = âˆ R

7. At point R extend line which intersects line L at S and draw a line RS.

Exercise 10.2 Page: 199

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

**Solution:-**

Steps of construction:

1. Draw a line segment YZ = 5 cm.

2. With Z as a center and radius 6 cm, draw an arc.

3. With Y as a center and radius 4.5 cm, draw another arc, cutting the previous arc at X.

4. Join XY and XZ.

Then, Î”XYZ is the required triangle.

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

**Solution:-**

Steps of construction:

1. Draw a line segment AB = 5.5 cm.

2. With A as a center and radius 5.5 cm, draw an arc.

3. With B as a center and radius 5.5 cm, draw another arc, cutting the previous arc at C.

4. Join CA and CB.

Then, Î”ABC is the required equilateral triangle.

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

**Solution:-**

Steps of construction:

1. Draw a line segment QR = 3.5 cm.

2. With Q as a center and radius 4 cm, draw an arc.

3. With R as a center and radius 4 cm, draw another arc, cutting the previous arc at P.

4. Join PQ and PR.

Then, Î”PQR is the required isosceles triangle.

**4. Construct Î”ABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure âˆ B.**

**Solution:-**

1. Draw a line segment BC = 6 cm.

2. With B as a center and radius 2.5 cm, draw an arc.

3. With C as a center and radius 6.5 cm, draw another arc, cutting the previous arc at A.

4. Join AB and AC.

Then, Î”ABC is the required triangle.

5. When we will measure the angle B of triangle by protractor, then angle is equal to âˆ B = 90^{o}

Exercise 10.3 Page: 200

**1. Construct Î”DEF such that DE = 5 cm, DF = 3 cm and mâˆ EDF = 90 ^{o}.**

**Solution:-**

Steps of construction:

1. Draw a line segment DF = 3 cm.

2. At point D, draw a ray DX to making an angle of 90^{o} i.e. âˆ XDF = 90^{o}.

3. Along DX, set off DE = 5cm.

4. Join EF.

Then, Î”EDF is the required right angled triangle.

**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 110 ^{o}.**

**Solution:-**

Steps of construction:

1. Draw a line segment AB = 6.5 cm.

2. At point A, draw a ray AX to making an angle of 110^{o} i.e. âˆ XAB = 110^{o}.

3. Along AX, set off AC = 6.5cm.

4. Join CB.

Then, Î”ABC is the required isosceles triangle.

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

**Solution:-**

Steps of construction:

1. Draw a line segment BC = 7.5 cm.

2. At point C, draw a ray CX to making an angle of 60^{o} i.e. âˆ XCB = 60^{o}.

3. Along CX, set off AC = 5cm.

4. Join AB.

Then, Î”ABC is the required triangle.

Exercise 10.4 Page: 202

**1. Construct Î”ABC, given m âˆ A =60 ^{o}, m âˆ B = 30^{o} and AB = 5.8 cm.**

**Solution:-**

Steps of construction:

1. Draw a line segment AB = 5.8 cm.

2. At point A, draw a ray P to making an angle of 60^{o} i.e. âˆ PAB = 60^{o}.

3. At point B, draw a ray Q to making an angle of 30^{o} i.e. âˆ QBA = 30^{o}.

4. Now the two rays AP and BQ intersect at the point C.

Then, Î”ABC is the required triangle.

**2. Construct Î”PQR if PQ = 5 cm, mâˆ PQR = 105 ^{o} and mâˆ QRP = 40^{o}.**

**(Hint: Recall angle-sum property of a triangle).**

**Solution:-**

We know that the sum of the angles of a triangle is 180^{o}.

âˆ´ âˆ PQR + âˆ QRP + âˆ RPQ = 180^{o}

= 105^{o}+ 40^{o}+ âˆ RPQ = 180^{o}

= 145^{o} + âˆ RPQ = 180^{o}

= âˆ RPQ = 180^{o}â€“ 145^{0}

= âˆ RPQ = 35^{o}

Hence, the measures of âˆ RPQ is 35^{o}.

Steps of construction:

1. Draw a line segment PQ = 5 cm.

2. At point P, draw a ray L to making an angle of 105^{o} i.e. âˆ LPQ = 35^{o}.

3. At point Q, draw a ray M to making an angle of 40^{o} i.e. âˆ MQP = 105^{o}.

4. Now the two rays PL and QM intersect at the point R.

Then, Î”PQR is the required triangle.

**3. Examine whether you can construct Î”DEF such that EF = 7.2 cm, mâˆ E = 110Â° and**

**mâˆ F = 80Â°. Justify your answer. **

**Solution:-**

From the question it is given that,

EF = 7.2 cm

âˆ E = 110^{o}

âˆ F = 80^{o}

Now we have to check whether it is possible to construct Î”DEF from the given values.

We know that the sum of the angles of a triangle is 180^{o}.

Then,

âˆ D + âˆ E + âˆ F = 180^{o}

âˆ D + 110^{o}+ 80^{o}= 180^{o}

âˆ D + 190^{o} = 180^{o}

âˆ D = 180^{o}â€“ 190^{0}

âˆ D = -10^{o}

We may observe that the sum of two angles is 190^{o} is greater than 180^{o}. So, it is not possible to construct a triangle.

Exercise 10.5 Page: 203

**1. Construct the Construct the right angled Î”PQR, where mâˆ Q = 90Â°, QR = 8cm and**

**PR = 10 cm.**

**Solution:-**

Steps of construction:

1. Draw a line segment QR = 8 cm.

2. At point Q, draw a ray QY to making an angle of 90^{o} i.e. âˆ YQR = 90^{o}.

3. With R as a center and radius 10 cm, draw an arc that cuts the ray QY at P.

4. Join PR.

Then, Î”PQR is the required right angled triangle.

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

**Solution:-**

Let us consider Î”ABC is a right angled triangle at âˆ B = 90^{o}

Then,

AC is hypotenuse = 6 cm â€¦ [given in the question]

BC = 4 cm

Now, we have to construct the right angled triangle by the above values

Steps of construction:

1. Draw a line segment BC = 4 cm.

2. At point B, draw a ray BX to making an angle of 90^{o} i.e. âˆ XBC = 90^{o}.

3. With C as a center and radius 6 cm, draw an arc that cuts the ray BX at A.

4. Join AC.

Then, Î”ABC is the required right angled triangle.

**3. Construct an isosceles right-angled triangle ABC, where mâˆ ACB = 90Â° and**

**AC = 6 cm.**

**Solution:-**

Steps of construction:

1. Draw a line segment BC = 6 cm.

2. At point C, draw a ray CX to making an angle of 90^{o} i.e. âˆ XCB = 90^{o}.

3. With C as a center and radius 6 cm, draw an arc that cuts the ray CX at A.

4. Join AB.

Then, Î”ABC is the required right angled triangle.

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