1. Construct ΔXYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm
Solution:
Steps of construction:
Step 1. Draw a line segment YZ = 5 cm.
Step 2. With Z as a center and radius 6 cm, draw an arc outside.
Step 3. With Y as a center and radius 4.5 cm, draw another arc, cutting the previous arc at X.
Step 4. Join XY and XZ.
Now, ΔXYZ is the required triangle.
Figure:
2. Construct an equilateral triangle of side 5.5 cm.
Solution:
Steps of construction:
Step 1. Draw a line segment AB = 5.5 cm.
Step 2. With A as a center and radius 5.5 cm, draw an arc outside.
Step 3. With B as a center and radius 5.5 cm, draw another arc, cutting the previous arc at C.
Step 4. Join CA and CB.
Now, ΔABC is the required equilateral triangle.
Figure:
3. Draw ΔPQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?
Solution:
Steps of construction:
Step 1. Draw a line segment QR = 3.5 cm.
Step 2. With Q as a center and radius 4 cm, draw an arc outside.
Step 3. With R as a center and radius 4 cm, draw another arc, cutting the previous arc at P.
Step 4. Join PQ and PR.
Now, ΔPQR is the required isosceles triangle.
Figure:
4. Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.
Solution:
Step 1. Draw a line segment BC = 6 cm.
Step 2. With B as a center and radius 2.5 cm, draw an arc outside.
Step 3. With C as a center and radius 6.5 cm, draw another arc, cutting the previous arc at A.
Step 4. Join AB and AC.
Now, ΔABC is the required triangle.
Figure:
Now, when we measure the angle B by the protector then we find that angle B is 90o
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