# PRACTICE QUESTIONS ON SIMILAR TRIANGLES

Question 1 :

Check if the triangle given below is similar. Solution :

Let us consider the triangles, AED and ACB

If two triangles are similar, then the ratio of its corresponding sides will be equal.

Condition :

2/(7/2)  ≠  3/5

4/7    3/5

So, the triangles AED and ACB are not similar.

Question 2 :

Find the value of x in the picture given below. In triangle PQC,

<PQC  =  180 - 110

<PQC  =  70

Now let us consider the triangles ABC and PQC.

<ABC  =  <PQC

<ACB  =  <PCQ

By using AA criterion, the above triangles are similar. Hence the ratio of their corresponding sides will be equal.

AB/PQ  =  BC/QC

5/x  =  (3+3)/3

5/x  =  6/3

5/x  =  2

x  =  5/2  =  2.5

Question 3 :

A girl looks the reflection of the top of the lamp post on the mirror which is 6.6 m away from the foot of the lamppost. The girl whose height is 1.25 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamppost are in a same line, find the height of the lamp post.

Solution : In triangles ABD and CED

<ABD  =  <ECD

By AA the above triangles are similar,

AB/ EC  =  BD/CD

x/1.25  =  6.6/2.5

x  =  6.6(1.25)/2.5

x  =  3.3 m

Hence the height of the lamp post is 3.3 m.

Question 4 :

A vertical stick of length 6 m casts a shadow 400 cm long on the ground and at the same time a tower casts a shadow 28 m long. Using similarity, find the height of the tower.

Solution :

Let us draw a rough diagram based on the given information. AB/ED  =  BC/DC

400 cm  =  4 m

AB/6  =  28/4

AB  =  (28/4)(6)

AB  =  42 m

Hence the height of the tower is 42 m.

Question 5 :

Two triangles QPR and QSR, right angled at P and S respectively are drawn on the same base QR and on the same side of QR. If PR and SQ intersect at T, prove that PT × TR = ST × TQ.

Solution : In triangles PTQ, and STR

<QPT  =  <RST  (A)

<PTQ  =  <STR (Vertically opposite angles)  (A)

So, the triangles PTQ and STR are similar.

PQ/SR  =  PT/TS  =  QT/RT

PT/TS  =  QT/RT

PT x RT  =  QT x TS

Hence proved. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

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

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

1. Click on the HTML link code below.

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 