Q6 (a) In the figure (1) given below, AB = AD, BC = DC. Find ∠ ABC. (b)In the figure (2) given below, BC = CD. Find ∠ACB. (c) In the figure (3) given below, AB || CD and CA = CE. If ∠ACE = 74° and ∠BAE =15°, find the values of x and y.
Q8 (a) In the figure (1) given below, ABC is an equilateral triangle. Base BC is produced to E, such that BC’= CE. Calculate ∠ACE and ∠AEC. (b) In the figure (2) given below, prove that ∠ BAD : ∠ ADB = 3 : 1. (c) In the figure (3) given below, AB || CD. Find the values of x, y and ∠.
Q9 In the given figure, D is mid-point of BC, DE and DF are perpendiculars to AB and AC respectively such that DE = DF. Prove that ABC is an isosceles triangle.
Q11 In a triangle ABC, AB = AC, D and E are points on the sides AB and AC respectively such that BD = CE. Show that: (i) ∆DBC ≅ ∆ECB (ii) ∠DCB = ∠EBC (iii) OB = OC,where O is the point of intersection of BE and CD.
Q12 ABC is an isosceles triangle in which AB = AC. P is any point in the interior of ∆ABC such that ∠ABP = ∠ACP. Prove that (a) BP = CP (b) AP bisects ∠BAC
Q14 (a) In the figure (i) given below, CDE is an equilateral triangle formed on a side CD of a square ABCD. Show that ∆ADE ≅ ∆BCE and hence, AEB is an isosceles triangle. (b) In the figure (ii) given below, O is a point in the interior of a square ABCD such that OAB is an equilateral trianlge. Show that OCD is an isosceles triangle.
