Question
(a) Construct ΔPQR, given ¯¯¯¯¯¯¯¯PQ=3.5 cm,¯¯¯¯¯¯¯¯PR=4.5 cm, and ¯¯¯¯¯¯¯¯¯QR=5.5 cmÂ
(b) Construct ΔPQR, when PQ = 4 cm, QR = 6 cm and ∠PQR = 60∘. [4 MARKS]
Answer: Option A
:
 Each part: 2 Marks
(a) Â Steps of construction:
Draw ¯¯¯¯¯¯¯¯PQ=3.5 cm
With P as the centre, draw an arc with the radius equal to 4.5 cm.
With Q as the centre, draw another arc with radius 5.5 cm to cut the previous arc at R.
Join R to P and Q.
PQR is the required triangle.
Thus, we see that if three sides of a triangle are given and the sum of any two sides is always more than the third side, then a triangle can be constructed. This is known as SSS criterion for construction of triangles.
(b)Â Â Steps of construction:
Step 1: Draw a line segment QR = 6 cm.
Step 2: Construct an angle of 60∘ at point Q.
Step 3: Draw an arc on the ray QX with Q as the centre and the radius equal to 4 cm.
Step 4: Name the point where the arc cuts the ray QX, as P.
Step 5: Join points P and R.
PQR is the required triangle.
      Â
Â
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:
 Each part: 2 Marks
(a) Â Steps of construction:
Draw ¯¯¯¯¯¯¯¯PQ=3.5 cm
With P as the centre, draw an arc with the radius equal to 4.5 cm.
With Q as the centre, draw another arc with radius 5.5 cm to cut the previous arc at R.
Join R to P and Q.
PQR is the required triangle.
Thus, we see that if three sides of a triangle are given and the sum of any two sides is always more than the third side, then a triangle can be constructed. This is known as SSS criterion for construction of triangles.
(b)Â Â Steps of construction:
Step 1: Draw a line segment QR = 6 cm.
Step 2: Construct an angle of 60∘ at point Q.
Step 3: Draw an arc on the ray QX with Q as the centre and the radius equal to 4 cm.
Step 4: Name the point where the arc cuts the ray QX, as P.
Step 5: Join points P and R.
PQR is the required triangle.
      Â
Â
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