CBSE Board Students Helpline

Exercise1 Example2 Example3 Example4 Exercise5 Arithmetic Progression Impotant Question ARITHMETIC PROGERESSIONS solved Example ARITHMETIC PROGERESSIONS Questions Arithmetic Progressions Test Paper ARITHMETIC PROGERESSIONS

Exercise 4 Exercis3 Exercis2 Exercis1 Example 16 Example 15 Example 14 Example 11 Example 10 Example 11 Example 9 Example 8 Example 7 Example 4 Example 3 Example 2 Critieria for similarities of two triangles Similar Triangles Important Questions

Exercise - 12 1.   In the given figure, PQ || BC, AP = 2.4cm, AQ = 2cm, QC = 3cm and BC = 6cm. Find AB and PQ. 2.   The diagonals AC and BD of a quadrilatereal ABCD intersect each other at O such that prove that the quadrilateral ABCD is traperzium. 3.   In   and   if AC = 4.8cm, find AE 4.   In the given figurer, PQ || BC and PR || CD, prove that     5.   In   is parallel to base BC, with D on AB and E on AC. If   find   6.   In the given figure, PQ || AB and PR || AC. prove that QR || BC. 7.   If three or more parallel lines, are intersected by two transversals, prove that the intercepts made by them on the trans versals are proportional. 8.   In the given figure, DE || AC and DC || AP, prove that   9.   In the given figure,     and DE || AB prove that AD = BE. 10.   In the given figure AB || CD. If OA = 3x - 19, OB = x - 4, OC = x - 3 and OD = 4cm, determine x.   Answers (10).   (x = 11 cm or 8 cm)        

Exercise - 16 1.   In     the bisector of     intersects the side AC at D. A line parallel to side AC intersects line segment AB, DB and CB at points P, R and Q respectively. Prove that AB X CQ = BC X AP PR X BQ = QR X BP 2.   ABCD is a quadrilateral in which AB = AD. The bisector of   intersects the side BC and CD respectively at E and F. Prove that the segment EF is parallel to the diagonal BD. 3.   In   and the bisector of     intersects AC at D. Prove that   4.   If the diagonal BD of a quadrilateral ABCD bisects both     show that   5.   D is the midpoint of side BC of     DE and DF are respectively bisectors of such that E and F lie on AB and AC, respectively. Prove that EF || BC. 6.   O is a point inside a   The bisector of     meet the sides AB, BC and CA in points D, E and F respectively. Prove that AD. BE. CF = DB. EC. FA 7.   In the adjoining figure,   , AD is bisector of   Prove that DE X (AB + AC) = AB X AC. 8.   If the bisector of an angle of a triangle bisect the opposit...

Exercise - 14 1.   Prove that the area of the equilateral triangles describe on the side of a square is half the are of the equilateral triangle describe on its diagonals. 2.   In the given figure     Also     If BC = 12cm, find QR. 3.   ABC is a triangle right angled at A, AD is perpendicular to BC. IF BC = 13cm and AC = 5cm, find teh ratio of the areas of     and   . 4.   The area of two similar triagles are 121cm 2   and 64cm 2   respectively. If the median of the first triangle is 12.1cm, find the correstponding median of the other. 5.   In an equilateral triangle with side a, prove that the area of the triangles is   6.   D and E are points on the sides AB and Ac respectively of     such that DE is parallel to BC and AD : DB = 4 : 5. CD and BE intersect each other at F. Find the ratio of the areas of     and   Answers (2)   6cm (3)   169 : 25 (4)   8.8cm (6)   16 : 81      

Exercise - 15 1.   The perpendicular AD on the base BC of a   intersects BC at D so that DB = 3CD. Prove that 2AB 2   = 2AC 2   + BC 2 . 2.   P and Q are points on the side CA and CB respectively of a   right angled at C.     Prove that AQ 2   + BP 2   = AB 2   + PQ 2. 3.   In   , if AD is the median, Show that AB 2   + AC 2   = 2(AD 2   + BD 2 ) 4.   PQR is an isosceles right triangle, right angled at R. Prove that PQ 2   = 2PR 2 . 5.   In a     is an acute angle and     Prove that AC 2   = AB 2   + BC 2   – 2BC. BD. 6.   In the adjoining figure, find the length of BD, If   7.   Prove that the altitude of an equilateral triangle of side   8.   P and Q are the midpoint of the sides CA and CB respectively of   right angled at C. Prove that 4(AQ 2   + BP 2 ) = 5AB 2 9.   In a triangle ABC, AD is perpendicular on BC. Prove that AB 2   + CD 2   = AC 2   + BD 2 10.   Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. 11.   In ad...