The document NCERT Solutions(Part - 1) - Practical Geometry Class 7 Notes | EduRev is a part of the Class 7 Course Mathematics (Maths) Class 7.

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**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: **

**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 .

**Question 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 2: **

**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.

It is the required construction.

**Question 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 3: **

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 ∠Q = ∠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 ∠P = ∠R.

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

Thus, we get parallelogram PQRS.

**Exercise 10.2 **

**Question 1: **

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

**Answer 1: **

**To construct: ** ΔXYZ, 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 ΔXYZ.

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

**Answer 2: **

**To construct: ** A ΔABC 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 ΔABC.

**Question 3: **

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

**Answer 3:**

**To construction: **ΔPQR, 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 ΔPQR.

**Question 4: **

**Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ****B. **

**Answer 4: **

**To construct: ** ΔABC 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 ΔABC where B = 80^{o}

**Exercise 10.3 **

**Question 1: ****Construct ΔDEF such that DE = 5 cm, DF = 3 cm and **∠**EDF = 90 ^{o} . **

**Answer 1: ****To construct:** ΔDEF where DE = 5 cm, DF = 3 cm and m ∠EDF = 90 .

**Steps of construction: **

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

(b) At point D, draw an angle of 90^{o} with the help of compass i.e., ∠XDF = 90^{o} .

(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.

**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 110 ^{o}.**

**Answer 2: ****To construct:** An isosceles triangle PQR where PQ = RQ = 6.5 cm and ∠Q = 110^{o}

**Steps of construction: **

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

(b) At point Q, draw an angle of 110^{o} with the help of protractor, i.e., ∠YQR = 110^{o}

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

(d) Join PR

It is the required isosceles triangle PQR.

**Question 3:**

**Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m **∠**C = 60 ^{o} . **

**Answer 3: **

**To construct: **ΔABC where BC = 7.5 cm, AC = 5 cm and m ∠C = 60** ^{o}** .

**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., ∠XCB = 60** ^{o}** .

(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.

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