Construct a triangle XYZ in which ZY = 30°, ZZ=90° and XY + YZ+ZX = 11 cm with steps of construction.
Answers
Answer:
Steps of Construction
(i) Draw a line segment AB = 11 cm.
(ii) At A, construct an angle of 30° and at B construct an angle of 90°.
(iii) Bisect these angles. Let bisector of these angles intersect at point X.
(iv) Draw perpendicular bisector CD of XA to intersect AB at Y and EF of XB to intersect AB at Z.
(v) Join XY and XZ to obtain required △XYZ.
Justification
Since Y lies on the perpendicular bisector of XA, Therefore,
YA = YX
⇒ ∠YAX = ∠YXA
Similarly, Z lies on the perpendicular bisector of XB. Therefore,
ZB = ZX
⇒ ∠ZBX = ∠ZXB
Now, AB = AY + YZ + ZB ⇒ AB = XY + YZ + ZX
In △XAY, we have
∠XYZ = ∠YXA + ∠YAX = 2∠YAX = ∠A
In XBZ, we have
∠XZY = ∠ZBX + ∠ZXB = 2∠ZBX = ∠B
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