The document Additional Questions Solutions- Constructions Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.

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**Question 1. Construct a triangle ABC in which BC = 7.5 cm, ∠ B = 45º and the difference between the other two sides is 4 cm. Solution: Steps of construction:**

I . Take BC = 7.5 cm.

II. Construct ∠CBX = 45º.

III. From cut off BD = 4 cm.

IV. Join D and C.

V. Draw the perpendicular bisector of DC which intersects at A.

VI. Join A and C.

Thus, ABC is the required triangle.

**Question 2. Construct a **Δ**ABC whose perimeter is 12 cm and sides are in the ratio 2 : 3 : 4. Solution: Steps of construction:**

I . Draw = 12 cm.

II. Draw , making an acute angle with XY in the downward direction.

III. From X, set off (2 + 3 + 4 = 9) nine equal distances along XZ.

IV. Mark points P, Q and R on XZ such that XP = 2 units PQ = 3 units QR = 4 units

V. Join RY.

VI. Draw QC || RY and PB || RY.

VII. With centre B and radius BX, draw an arc.

VIII. With centre C and radius CY, draw an arc which intersects previous arc at A.

IX. Join AB and AC.

Thus, ΔABC is the required triangle.

**Question 3. Construct ΔABC, in which ∠ B = 60º and ∠ C = 45º and the perpendicular from the vertex A to the base BC is 5.2 cm. Solution: Steps of construction:**

I . Draw a line PQ.

II . Mark a point L on PQ.

III. Draw LM ⊥ PQ.

IV. From cut off LA = 5.2 cm.

V. Draw XY || PQ, through A.

VI. Construct ∠XAB = 60º and ∠YAC = 45º meeting PQ at B and C respectively.

Thus, ΔABC is the required triangle.

**Question 4. Contruct an equilateral triangle if its altitude is 6 cm. Give justification for your construction. Solution: Steps of construction:**

I . Draw a line XY and mark a point D on it.

II. Construct perpendicular PD on XY.

III. Cut off AD = 6 cm

IV. Make ∠CAD = 30° and ∠BAD = 30° at A on both sides of AD, such that B and C lie on XY.

Thus, ABC is the required triangle.**Justification: **

∵ ∠CAD = 30° and ∠ADC = 90°

∴ In ΔADC, ∠C = 180 ∠ (90° + 30°) = 60°

Similarly, ∠B = 60° Also, ∠BAD + ∠CAD = 60°

⇒ ∠A = 60°

Thus, ΔABC is an equilateral triangle in which altitude AD = 6 cm.

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