Subject: MathematicsClass 10thSimilar triangles 1
1.Find the area of a right angled triangle. If the radius of its circumstances is 3 cm and altitude drawn on the hypotenuse is 2 cm.
2.PQ is drawn parallel to BC cutting the other two sides of ABC at P.Q. respectively such that AB = 2.4 cm BC = 3.5 cm, AC = 2.8 cm.
(a) If P divides AB internally in the ratio 5:3, calculate the lengths of AP, PB, AQ and QC.
(b) If P divides ABC externally in the ratio 5:3, calculate the lengths of AP, PB, AQ and QC.
3.In the fig (1), AB = 6 cm, CD = y, AC = 4 cm, CF = x cm, EF = 10 cm, calculate the values of x and y.
4.ABC is right angled at A and AD is drawn perpendicular to BC. Show that arABD/ACD =.
5.In the fig (2)the diagram shows two isosceles triangles which are similar, PQ, BC are not parallel, PC = 4 cm, AQ = 3 cm, BC = 15 cm. Calculate the (a) length of A. P. (b) the ratio of the area of s APQ & ABC assuming that AP = PQ.
6.Any point X inside DEF is joined to its vertices. From a point P in DX, PQ is drawn parallel to DE meeting XE at Q and QR is drawn parallel to EF meeting XF at R. Prove that
7.Sides of a are 4 cm, and 6 cm. the perimeter of a similar triangle is 30 cm. Find the lengths of this.
8.In the fig (3)PA, BQ & RC are prove that 1/x+ 1/y= 1/z.
9.In the fig (4) AO/OC = BO/OD = ½, AB = 5 cm, find DC.
Fig 3
Subject: MathematicsClass 10thSimilar triangles 1
10.A trapezium ABCD is which. Diagonals AC & BD intersect at E. Also AED~BEC, prove that AD = BC.
12.P, Q is the points on the sides AB & AC respectively of ABC. . If AP 2 cm BP = 4 cm, AQ = 3 cm, QC = 6 cm show that BC = 3PQ.
13.In a quadrilateral ABCD, if the bisectors of <ABC and ADC meet each other on the diagonal AC. Prove that the bisectors of <BAD & <BCD will meet each other on the diagonal BD.
14.In PQR, PQ = PR, X is a point on PR such that. Prove that OX = OR.
15.In fig (6) DEFG is a square and <BAC is a right angle. Prove that .
16.In fig (7) , prove that
17.In a right angle with sides ‘a’ and ‘b’ and hypotenuse ‘c’. The altitude drawn on the hypotenuse is x. Prove that ab = cx.
18.The hypotenuse of a right angle is 6 cm more that twice the shortest side. If the third side is 2 cm less that the hypotenuse, find the sides of the triangle.
19.In fig (8) D is the mid point of BC of ABC, AD is bisected at point E and BF produced cuts AC at X. Prove that BE:EX = 3:1 [hint: drawn ].
20.In fig (9) ABCD is a cyclic quadrilateral whose sides AB & DC when produced meet at O. The bisector of <AOD meets BC at P and AD at A. Prove that BP/PC = DQ/QA.
Subject: MathematicsClass 10thSimilar triangles 1
21.ABC & DBC are two triangles on the opposite sides of the same base BC. AD joined meets BC at O. Prove that arABC/arDBC = OA/OD.