The document Ex 11.2 NCERT Solutions- Constructions Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.

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**Q1. Construct a triangle ABC in which BC = 7 cm, ∠B = 75º and AB + AC = 13 cm.Ans: Steps of construction:**

- Draw a ray BX.
- From cut off = 7 cm.
- At B, construct ∠CBY = 75º.
- From cut off BD = 13 cm (= AB + BC)
- Join D and C.
- Bisect DC such that the bisector of DC meets BD at A.
- Join AC.

Thus, ΔABC is the required triangle.

**Q2. Construct a triangle ABC in which BC = 8 cm, ∠ B = 45º and AB ∠ AC = 3.5 cm.Ans: Steps of construction: **

- Draw a ray
- From , cut off BC = 8 cm.
- Construct ∠CBY = 45º.
- From cut off = 3.5 cm.
- Join D and C.
- Draw PQ, the perpendicular bisector of DC, which intersects at A.
- Join AC.

Thus, ABC is the required triangle.

**Q3. Construct a triangle PQR in which QR = 6 cm, ∠Q = 60º and PR ∠ PQ = 2cm.Ans: Steps of construction:**

- Draw a ray .
- From , cut off QR = 6 cm.
- Construct a line YQY' such that ∠RQY = 60º.
- Cut off QS = 2 cm (from QY').
- Join ‘S’ and ‘R’.
- Draw MN, the perpendicular bisector of SR, which intersects QY at P.
- Join P and R.

Thus, PQR is the required triangle.

**Q4. Construct a triangle XYZ in which ∠ Y = 30º , ∠ Z = 90º and XY + YZ + ZX = 11 cm.Ans: Steps of construction:**

- Draw a line segment AB = 11 cm = (XY + YZ + ZX)
- Construct ∠BAP = 30º = ∠Y
- Construct ∠ABQ = 90º = ∠Z
- Draw , the bisector of ∠BAP.
- Draw , the bisector of ∠ABQ, such that and intersect each other at X.
- Draw perpendicular bisector of AX, which intersects AB at Y.
- Draw perpendicular bisector of XB, which intersects AB at Z.
- Join XY and XZ.

Thus, XYZ is the required triangle.

**Q5. Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.Ans: Steps of construction:**

- Draw = 12 cm.
- Construct ∠CBY = 90º.
- From cut off BX = 18 cm.
- Join CX.
- Draw PQ, the perpendicular bisector of CX, such that PQ meets BX at A.
- Join AC.

Thus, ABC is the required triangle.

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