∆ 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?
Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆ PQR (see Fig. 7.40). Show that:
(i) ∆ BM≅∆ PQN
(ii) ∆ ABC≅∆ PQR
Which separation techniques will you apply for the separation of the following?
(a) Sodium chloride from its solution in water (b) Ammonium chloride from a mixture containing sodium chloride and ammonium chloride (c) Small pieces of metal in the engine oil of a car (d) Different pigments from an extract of flower petals (e) Butter from curd (f) Oil from water (g) Tea leaves from tea(h) Iron pins from sand (i) Wheat grains from husk (j) Fine mud particles suspended in water
