NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

NCERT Solutions for class 7 maths chapter 10 practical geometry exercise 10.1
Question: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:

1. Draw the line AB

2. Mark any point C outside AB and a point D on AB

3. Join CD

4. Draw an arc with convenient radius with D as centre cutting AB at E and DC at F

5. With the same radius as in step 4 draw an arc IGH with C as a centre and cutting line AC at G.

6 Place one tip of the compass on E and adjust the opening so that pencil tip touches at F.

7. With the same opening in step 6 and G as centre cut an arc at J on IGH.

8. Join CJ and extend the line. This line will be parallel to AB

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

Answer:

1. Draw a line l. Mark a point P on the line

2. With p as a centre and with any radius draw an arc which touches the line at A and B

3. Take a length more than AP with A as centre draw an arc. with the same length on compass and B as centre draw an arc to cut the previous arc at Q.

4. Join PQ. PQ is perpendicular to the line l

5. Take 4 cm on the compass and with P as centre cut an arc on line PQ at C. The length PC=4 cm

6. with P as a centre and any radius, draw an arc to cut line l at D and PQ at E.

7. with the same radius as in step 6 draw an arc GF with centre C so that it cuts the line PQ at G.

8. Take the length DE on the compass and with G as centre draw an arc to cut FG at J

9. Join CJ and extend the line to name it as line m. Now the line l is parallel to line m

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

Answer:

1. Draw the line PQ parallel to l using the steps to draw parallel lines

2. Draw the line RS parallel to PQ using the steps to draw parallel lines

the two parallel lines make the shape of a parallelogram PQRS.

NCERT solutions for class 7 maths chapter 10 practical geometry exercise 10.2

Question:1 Construct in which XY= 4.5 cm, YZ = 5 cm and ZX = 6 cm.

Answer:

in which XY= 4.5 cm, YZ = 5 cm and ZX = 6 cm :

1. Draw a line XY = 4.5 cm

2. with x as centre and length= 6cm draw an arc

3. with y as centre and length = 5cm draw another arc to cut the arc drawn in step 2 at Z

4. Join XZ and YZ. XYZ is the required triangle

Question:2 Construct an equilateral triangle of side 5.5 cm.

Answer:

an equilateral triangle of side 5.5 cm :

1. Draw a line AB = 5.5 cm

2. with A as centre and length= 5.5cm draw an arc

3. with B as centre and length = 5.5cm draw another arc to cut the arc drawn in step 2 at C

4. Join AC and BC.ABC is the required triangle

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

Answer:

PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm:

1.Draw a line QR = 3.5 cm

2. With Q as centre and length = 4 cm draw an arc

3. With R as centre and length = 4cm draw another arc to cut the previous arc at P

4. Join QP and QR. Then PQR is the required triangle

As we can see two sides of the triangle are same so The triangle is an isosceles triangle.

Question:4 Construct such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure .

Answer:

such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure :

1. Draw a line AB = 2.5 cm

2. with A as centre and length= 6.5cm draw an arc

3. with B as centre and length = 6cm draw another arc to cut the arc drawn in step 2 at C

4. Join AC and BC. ABC is the required triangle

On measuring angle B comes out to be 90 degrees.

NCERT solutions for class 7 maths chapter 10 practical geometry exercise 10.3

Question:1 Construct such that DE = 5 cm, DF = 3 cm and .

Answer:

such that DE = 5 cm, DF = 3 cm and :

1. Draw a line DE = 5cm

2. Draw a line DX making 90 degrees with DE.

3. cut the length DF =3cm using the compass on the line DX

4. Join E and F

DEF is the required triangle

Question: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 .

Answer:

1. Draw a line DE = 6.5 cm

2. Draw a line DX making 110 degrees with DE.

3. cut the length DF =6.5 cm using the compass on the line DX

4. Join E and F

DEF is the required triangle

Question:3 Construct with BC = 7.5 cm, AC = 5 cm and .

Answer:

with BC = 7.5 cm, AC = 5 cm and :

1. Draw a line AC = 5 cm

2. Draw a line CX making 60 degrees with AC from C.

3. cut the length BC =7.5 cm using the compass on line CX

4. Join A and B

ABC is the required triangle

NCERT solutions for class 7 maths chapter 10 practical geometry exercise 10.4

Question:1 Construct , given , and AB = 5.8 cm.

Answer:

, given , and AB = 5.8 cm :

1. Draw the line AB=5.8 cm

2. At A making an angle 60 degrees with AB draw a line AX

3. At B making an angle 30 degrees with AB draw a line BY

4. The lines AX and BY intersect at C ( in case the drawn line AX or BY is small extend it to intersect each other)

ABC is the requires triangle

Question:2 Construct if PQ = 5 cm, and .

Answer:

if PQ = 5 cm, and :

the sum of angles of a triangle is 180 degrees. Given angles PQR and QRP, so the angle QPR= 180-(105+40)=35 degrees

1. Draw the line PQ=5 cm

2. At Q making an angle 105 degrees with PQ draw a line QY

3. At P making an angle 35 degrees with PQ draw a line PX

4. The lines PX and QY intersect at R ( in case the drawn line PX or QY is small extend it to intersect each other)

PQR is the required triangle

Question:3 Examine whether you can construct such that EF = 7.2 cm, and . Justify your answer.

Answer:

No, we cannot construct such that EF = 7.2 cm, and . This is because of the property of the triangle of having a sum of internal angles equal to 180 degrees. if we have , then we cannot have because then the sum would exceed 180 degree which is impossible.

NCERT solutions for class 7 maths chapter 10 practical geometry exercise 10.5

Question:1 Construct the right angled , where , QR = 8cm and PR = 10 cm.

Answer:

the right-angled , where , QR = 8cm and PR = 10 cm:

1. Draw QR = 8 cm

2. Draw a perpendicular QX to QR at Q

3. From R and with length = 10 cm cut an arc on QX. The arc meet QX at P

4. Join PR

PQR is the required triangle

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

Answer:

a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long:

1. Draw QR = 4 cm

2. Draw a perpendicular QX to QR at Q

3. From R and with length = 6 cm cut an arc on QX. The arc meet QX at P

4. Join PR

Triangle PQR is the required triangle

Question:3 Construct an isosceles right-angled triangle ABC, where and AC = 6 cm.

Answer:

1. Draw CA = 6 cm

2. Draw a perpendicular CX to CA at C

3. From C and with length = 6 cm cut an arc on CX. The arc meet CX at B

4. Join BA

Triangle ABC is the required triangle