∆ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠ BCD is a right angle.
Length (in mm)
Number of leaves
118 − 126
3
127 − 135
5
136 − 144
9
145 − 153
12
154 − 162
163 − 171
4
172 − 180
2
(i) Draw a histogram to represent the given data. (ii) Is there any other suitable graphical representation for the same data? (iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
∆ ABC and ∆ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig.). If AD is extended to intersect BC at P, show that
(i) ∆ABD ≅ ∆ACD
(ii) ∆ABP≅ ∆ACP
(iii) AP bisects ∠A as well as ∠D.
(iv) AP is the perpendicular bisector of BC.
AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC
(ii) AD bisects ∠A.
When 3.0g of carbon is burnt in 8.00g oxygen, 11.00g of carbon dioxide is produced. What mass of carbon dioxide will be formed when 3.00g of carbon is burnt in 50.0g of oxygen? Which law of chemical combination will govern your answer?
Length (in hours)
Number of lamps
300 − 400
14
400 − 500
56
500 − 600
60
600 − 700
86
700 − 800
74
800 − 900
62
900 − 1000
48
(i) Represent the given information with the help of a histogram. (ii) How many lamps have a lifetime of more than 700 hours?
