Skip to main content

Similar Triangles

Similar Triangles

Whenever we talk about two congruent figures then they have the ‘same shape’ and the ‘same size’. There are figures that are of the ‘same shape but not necessarily of the ‘same size’. They are said to be similar. Congruent figures are similar but the converse is not true

All regular polygons of same number of sides are similar. They are equilateral triangles, squares etc. All circles are also similar.

Two polygons of the same number of sides are similar if their corresponding angles are sides are proportional.

Two triangles are similar if their corresponding are equal and corresponding sides are proportional.

Basic Proportionality Theorem or Thales Theorem.

Theorem-1

If a line is drawn parallel to one side of a triangle, to interest the other two sides indistinct points, the other two sides are divided in the same ratio.

Given: - In 

To prove:- 

Construction:- BE and CD are joined.  and  are drawn.

Proof:-

But 

as they are on the same base DE and 

 from (1), (2) and (3) we get 

Corollary: In  then

Proof:- We know


(Taking reciprocals)

Multiplying (1) and (2) we get

 

 


Labels:

Comments

Post a Comment

Popular posts from this blog

The Missing Mail | Class IX - Interact in English

NCERT / CBSE Literature Reader for English Course (Communicative) Important Exercise Questions Q.3: (a) Why is Ramanujam worried about getting his daughter married? Give four reasons. (b) How does the postman console and guide Ramanujam and his family during each of the instances you have listed in 3 (a)? Ans 3(a): Ramanujam is worried as he could not find a suitable match to marry his daughter off which was getting delayed because of different reasons. The four causes of his worriedness are - (i) Sometimes horoscopes did not match, (ii) Sometimes the girl’s appearance were not approved, (iii) At times there were problems of too much dowry and other financial matters, (iv) The season was closing with only three more auspicious dates left, whereas, he was not able to finalise any alliance by that time. Ans 3(b): First instance - When Ramanujam said that horoscopes did not agree Thanappa consoled and guided him by saying that he should not utter inauspicious words and when the God wills ...
Post a Comment
Read more

The Tribute - Multiple Choice Questions

Question (1):   What does the word 'petite' mean? 1. strong 2. small 3. neat 4. clean Ans:   2 Question (2):   What was almost a routine affair for Babuli during his student days? 1. working in the city 2. writing to his elder brother 3. going home in the rickety bus 4. reading big books Ans:   3 Question (3):   What was written in the elder brother's letter? 1. That they were missing him in the village 2. That there was to be a partition 3. That there was a festival 4. That he would get money Ans:   2 Question (4):   How many days were left for the partition? 1. A week 2. A month 3. A day 4. Three days Ans:   1 Question (5):   How much money was expected for Babuli's land? 1. Seven thousand 2. Twenty thousand 3. Ten thousand 4. Forty thousand Ans:   2 Question (6):   What makes Babuli think of the butcher? 1. Hunger 2. Wife's heartlessness 3. The i...
Post a Comment
Read more

ENGLISH (Communicative) Sample Question Paper 5

Sample Paper – 2009 Class – XSubject – ENGLISH (Communicative) General instructions: The paper consist of FOUR sections: SECTION A (READING) - 20 Marks SECTION B (WRITING) - 30 Marks SECTION C (GRAMMAR) - 20 Marks SECTION D (LITERATURE) - 30 Marks Attempt all the questions. Do not write anything on the question paper. All the answers must be correctly numbered as in the question paper. And written in the answer sheets provided to you. Attempt all questions in each section before going on to the next section. Read each question carefully and follow the instructions. Strictly adhere to the word limit given with each question. Marks will be deducted for exceeding the word limit. SECTION A (READING) – 20 MARKS A1. Read the following passage and answer the following questions: [12] THE TUITION TRAP 1. Given the general awareness of the woeful condition of our State sch...
1 comment
Read more