**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 AD^{2} = 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.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**