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Construct a ∆XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm. How will you verify your answer?

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Steps of Construction: 

1. Draw a line segment AB = 11 cm (XY + YZ + ZX= 11 cm) 

2. Construct an angle of 30° at the point A. 

3. Construct an angle of 90° at the point B. 

4. Bisect these two angles at A and B respectively and let their bisectors meet at the point X. 

5. Draw a perpendicular bisector CD of AX and EF of XB to intersect AB at point Y and Z respectively. Join X, Y and X, Z. 

Thus, ∆XYZ is the required triangle. 

Verification: Measure the sides XY, YZ and ZX of ∆XYZ. It is found that XY + YZ + ZX= 11 cm.

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