Exercise 13.2

1. Construct ΔABC in which BC = 7 cm, ∠B = 75° and AB + AC = 12 cm.

Sol:

Fig

1. Draw a line segment BC =7 cm

2. Erect ∠B = 75°

3. Mark a point D on BX such that BD = AB + AC

4. Join D, C and draw the perpendicular bisectors of CD meeting BD at A.

5. Join A to C to form the ΔABC.

2. Construct ΔPQR in which QR = 8 cm, ∠Q = 60° and PQ − PR = 3.5 cm

Sol:

Fig

1. Draw QR = 8 cm

2. Construct ∠RQX = 30° at Q

3. Mark a point S on QX such that QS = PQ - PR = 3.5 cm

4. Join S, R and draw the perpendicular bisector to $$\overline{QR}$$ meeting QX at P.

3. Construct Δ XYZ in which ∠Y = 30°, ∠Z = 60° and XY + YZ + ZX = 10 cm.

Sol:

Fig

1. Draw a line segment AB = XY + YZ + ZX = 10 cm

2. Construct  ∠BAP = $$\frac{1}{2}$$∠Y at A and ∠ABQ = $$\frac{1}{2}$$∠Z at B meeting at X.

3. Draw the perpendicular bisectors to XA and XB meeting $$\overline{AB}$$ at Y and  Z respectively.

4. Join X to Y and Z to form the ΔXYZ.

4. Construct a right triangle whose base is 7.5cm. and sum of its hypotenuse and other side is 15cm.

Sol:

Fig

1. Draw BC = 7.5 cm

2. Construct ∠CBX = 90° 

3. Mark a point D on BX such that BD = 15 cm

4. Join C, D.

5. Draw the perpendicular bisectors of $$\overline{CD}$$ meeting BD at A.

6. Join A, C to form the ΔABC.

5. Construct a segment of a circle on a chord of length 5cm. containing the following angles.

i.90°

ii.45°

iii.120°

Sol:

i.90°

Fig

Draw a line segment BC =5 cm

Draw the perpendicular bisectors of BC meeting $$\overline{BC}$$ at O.

Draw an arc of radius OB or OC with center O.

Mark any point A on the arc and join it with B and C.

∠BAC = 90°.

ii.45°

Fig

Draw a line segment BC =5 cm

Construct ΔBOC such that BC =5 cm, ∠B = 45° = ∠C

Draw a circle segment of radius OB or OC with center O

Mark any point A on the segment and join it with B and C.

iii.120°

Fig

Draw a line segment AB =5 cm

Construct ΔAOB in which ∠A = 30°,∠B = 30°; AB =5 cm

With O center draw a circle segment.

On the opposite side make any point  C and join it with B and C.

∠ACB = 120°.