Chapter 10 Practical Geometry Exercise 10.4
Question 1: Construct ΔABC, given m ∠A =60°, m ∠B = 30° and AB = 5.8 cm.
Answer:
Rough Figure
Actual Figure
Steps of Construction
1. Draw AB = 5.8 cm.
2. Take A as a centre draw an angle at A such that ∠QAB = 60°.
3. Take B as a centre draw an angle at B such that ∠PBA = 30°.
4. AQ, BP are intersecting at C.
5. ⃤ ABC is our required triangle.
Question 2: Construct ΔPQR if PQ = 5 cm, m∠PQR = 105o and m∠QRP = 40o.
(Hint: Recall angle-sum property of a triangle).
Answer:
(by angle sum property)
∠P + ∠Q + ∠R = 180°
∠P + 105° + 40° = 180°
= 180° - (105° + 40°)
= 180° - 145° = 35°
∠P = 35°
Rough Figure
Actual Figure
Steps of Construction
1. Draw PQ = 5 cm.
2. Take P as a centre draw an angle at P such that ∠XPQ = 35°.
3. Take Q as a centre draw an angle at Q such that ∠YQP = 105°.
4. XP, YQ are intersecting at R.
5. ⃤ PQR is our required triangle.
Question 3: Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠E = 110° and m∠F = 80°. Justify your answer.
Answer:
(by angle sum property)
∠E + ∠F = 110° + 80° = 190° ≠ 180°
The angle of ⃤ DEF are not satisfying by angle sum property. So, we can’t construct the given triangle.
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