Question

1. consider a triangle abc.

measure the lengths of its
sides ab, bc, and ca using
a ruler. then verify the triangle
inequality theorem.

1. draw a circle. mark three non -

collinear points on its
circumference. form a triangle
with these three points.
measure the sides of the
triangle and verify the triangle
inequality theorem.

1. draw a circle. measure its

radius as r = 3 cm (using a
ruler). then draw its diameter
and measure it. verify the
relation d = 2r.

Explanation:

Step1: Measure the sides of triangle ABC

Use a ruler to measure the lengths of \(AB\), \(BC\), and \(CA\). Let's assume \(AB = a\), \(BC = b\), \(CA = c\).

Step2: Verify the triangle - inequality theorem

Check if \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step3: Draw a circle and mark non - collinear points

Draw a circle. Mark three non - collinear points \(P\), \(Q\), \(R\) on its circumference. Form triangle \(PQR\). Measure the sides \(PQ=m\), \(QR = n\), \(RP=p\).

Step4: Verify the triangle - inequality theorem for triangle \(PQR\)

Check if \(m + n>p\), \(m + p>n\), and \(n + p>m\).

Step5: Draw a circle with radius \(r = 3\mathrm{cm}\)

Use a compass to draw a circle with radius \(r = 3\mathrm{cm}\) (measured with a ruler).

Step6: Draw the diameter and measure it

Draw a diameter of the circle. Let the length of the diameter be \(d\). According to the formula \(d = 2r\), when \(r = 3\mathrm{cm}\), we expect \(d=6\mathrm{cm}\). Measure \(d\) with a ruler to verify.

Answer:

1. After measuring the sides of \(\triangle ABC\) (say \(AB = 4\mathrm{cm}\), \(BC=5\mathrm{cm}\), \(CA = 6\mathrm{cm}\)), we check: \(4 + 5>6\) (\(9>6\)), \(4+6>5\) (\(10 > 5\)), \(5 + 6>4\) (\(11>4\)).
2. For the triangle formed by three non - collinear points on the circle (say \(PQ = 3\mathrm{cm}\), \(QR=4\mathrm{cm}\), \(RP = 5\mathrm{cm}\)), we check: \(3+4>5\) (\(7>5\)), \(3 + 5>4\) (\(8>4\)), \(4+5>3\) (\(9>3\)).
3. When \(r = 3\mathrm{cm}\), using the formula \(d = 2r\), \(d = 6\mathrm{cm}\). Measuring the diameter of the circle (drawn with radius \(r = 3\mathrm{cm}\)) with a ruler should give \(d = 6\mathrm{cm}\).