Basic Proportionality Theorem Practice Questions Worksheet :
Here we are going to see some practice problems based on proportionality theorem
(1) In ΔABC, D and E are points on the sides AB and AC respectively such that DE ∥ BC
(i) If AD/DB = 3/4 and AC = 15 cm find AE. Solution
(ii) If AD = 8x −7 , DB = 5x −3 , AE = 4x −3 and EC = 3x −1 find the value of x. Solution
(2) ABCD is a trapezium in which AB || DC and P,Q are points on AD and BC respectively, such that PQ || DC if PD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD
(3) In ΔABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE ||BC
(i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm.
(ii) AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm.
(4) In fig. if PQ || BC and PR || CD prove that
(i) AR/RD = AQ/AB
(ii) QB/AQ = DR/AR Solution
(5) Rhombus PQRB is inscribed in ΔABC such that ÐB is one of its angle. P, Q and R lie on AB, AC and BC respectively. If AB = 12 cm and BC = 6 cm, find the sides PQ, RB of the rhombus
(6) In trapezium ABCD, AB || DC , E and F are points on non-parallel sides AD and BC respectively, such that EF || AB . Show that AE/ED = BF/FC
(7) In figure DE || BC and CD || EF. Prove that AD2 = AB×AF
(8) In ΔABC, AD is the bisector of <A meeting side BC at D, if AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC
(9) Check whether AD is bisector of <A of ΔABC in each of the following
(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm.
(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm.
(10) In figure <QPR = 90° , PS is its bisector. If ST ⊥ PR, prove that ST × (PQ + PR) = PQ × PR.
(11) ABCD is a quadrilateral in which AB=AD, the bisector of <BAC and <CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF BD .
After having gone through the stuff given above, we hope that the students would have understood, how to solve problems using Basic Proportionality Theorem.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Converting customary units worksheet
Customary units worksheet
Integers and absolute value worksheets
Nature of the roots of a quadratic equation worksheets
Trigonometry heights and distances
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Converting repeating decimals in to fractions