**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 :

AE/AC = AD/AB

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

<ADB = <EDC

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**

We always appreciate your feedback.

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 **

**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**