Mathematics
In the adjoining figure, verify by measurement that:
(i) AC + BD = AD + BC
(ii) AB + CD = AD - BC
Answer
On measuring the given line segments with the help of a ruler, we get:
AB = 2 cm, BC = 1 cm, CD = 1.5 cm, AC = 3 cm, BD = 2.5 cm, AD = 4.5 cm
(i) AC + BD = 3 cm + 2.5 cm = 5.5 cm
AD + BC = 4.5 cm + 1 cm = 5.5 cm
∴ AC + BD = AD + BC is verified.
(ii) AB + CD = 2 cm + 1.5 cm = 3.5 cm
AD - BC = 4.5 cm - 1 cm = 3.5 cm
∴ AB + CD = AD - BC is verified.
Related Questions
If A, B and C are collinear points such that AB = 6 cm, BC = 4 cm and AC = 10 cm, which one of them lies between the other two?
In the adjoining figure, verify the following by measurement:
(i) AB + BC = AC
(ii) AC - BC = AB
In the adjoining figure, measure the lengths of the sides of the triangle ABC and verify:
(i) AB + BC > AC
(ii) BC + AC > AB
(iii) AC + AB > BC
What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from:
(i) 4 to 10
(ii) 2 to 5
(iii) 7 to 10
(iv) 8 to 5
(v) 11 to 5
(vi) 6 to 3
Also find the number of right angles turned in each case.