CBSE > Class 10 | CBSE Board | Homework Help

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

Construction
Join the vertex B of {tex}\triangle{/tex}ABC to Q and the vertex C to P to form the lines BQ and CP and then drop a perpendicular QN to the side AB and also draw PM{tex}\perp{/tex}AC as shown in the given figure.

Proof
Now the area of {tex}\triangle{/tex}APQ = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} AP {tex}\times{/tex} QN (Since, area of a triangle = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} Base {tex}\times{/tex} Height)
Similarly, area of {tex}\triangle{/tex}PBQ = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} PB {tex}\times{/tex} QN
area of {tex}\triangle{/tex}APQ = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} AQ {tex}\times{/tex} PM
Also, area of {tex}\triangle{/tex}QCP = {tex}\frac {1}{2}{/tex} {tex}\times{/tex} QC {tex}\times{/tex} PM ...(i)
Now, if we find the ratio of the area of triangles {tex}\triangle{/tex}APQand {tex}\triangle{/tex}PBQ, we have
{tex}\frac{\text { area of } \Delta A P Q}{\text { area of } \Delta P B Q}{/tex} = {tex}\frac{\frac{1}{2} \times A P \times Q N}{\frac{1}{2} \times P B \times Q N}=\frac{A P}{P B}{/tex}
Similarly, {tex}\frac{\text { area of } \Delta A P Q}{\text { area of } \Delta Q C P}{/tex} = {tex}\frac{\frac{1}{2} \times A Q \times P M}{\frac{1}{2} \times Q C \times P M}=\frac{A Q}{Q C}{/tex} ...(ii)
According to the property of triangles, the triangles drawn between the same parallel lines and on the same base have equal areas.
Therefore, we can say that {tex}\triangle{/tex}PBQ and {tex}\triangle{/tex}QCP have the same area.
area of {tex}\triangle{/tex}PBQ = area of {tex}\triangle{/tex}QCP ...(iii)
Therefore, from the equations (i), (ii) and (iii) we can say that,
{tex}\frac{{AP}}{{PB}} = \frac{{AQ}}{{QC}}{/tex}
Also, {tex}\triangle{/tex}ABC and {tex}\triangle{/tex}APQ fulfil the conditions for similar triangles, as stated above. Thus, we can say that {tex}\triangle{/tex}ABC {tex} \sim {/tex} {tex}\triangle{/tex}APQ.
The MidPoint theorem is a special case of the basic proportionality theorem.
According to mid-point theorem, a line drawn joining the midpoints of the two sides of a triangle is parallel to the third side.

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find the point on y axis which is equidistant from the point (5 -2) and (-3 2)

Posted by Saloni Dubey 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Kavya Chanana 4 years, 8 months ago

-3/5

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Use Euclid division algorithm to find the HCF of : 135 and 225

Posted by Ishika Singh 4 years, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Preet Bhullar 4 years, 8 months ago

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Madhav Dixit 4 years, 8 months ago

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Deepak Kumar 4 years, 8 months ago

HCF IS 45

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Pls give gujarati papers

Posted by Sreenandhika Nair 4 years, 8 months ago

CBSE > Class 10 > Regional Language

0 answers

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Wordsworth has said"Child is the father of man". Explain with reference to Bholi

Posted by Tamana Rahar 4 years, 8 months ago

CBSE > Class 10 > English Language and Literature

2 answers

Tamana Rahar 4 years, 8 months ago

Thank you sir

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Bipin Kumar 4 years, 8 months ago

Wordsworth say this statement , it's a worth statement. Firstly, describe about ideas of Wordsworth He wants to say that The child who is growing now on they are father of man as he expects that child is more carer about man And do what he/she wants in good sense. For Bholi Bholi was the main character of the story. She is described perfectly in the poem? It can be described as when Bholi was used to speak having some stammering, at that time none looked after it after her school when she reached her marriage life. In her marriage day, when her expected husband. When her expected husband asked for 5000 money . Meanwhile, Bholi was gazing at hum, when he wore Garland then she slipped her hand and throw Garland on fire and said I don't have to marry this man. This shows that Bholi, as daughter saved herself from being ruins and she also saved father from being ruins. Here, it shows that child, Bholi saved her life as well as her father and later he addded that she would serve her father and mother until death. ?? I expect that It's right right article.

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Your friend has sent you a letter 2 weeks ago by registered post . It had some important documents in it. Till date you received the letter . Write a letter to the post master of your local post office explaining the situation

Posted by Priya Ranga 4 years, 8 months ago

CBSE > Class 10 > English Language and Literature

0 answers

ANSWER

Why is agriculture called mainstay na of Indian economy suggest any three measures to enhance the agricultural production in India

Posted by Krithika Krithika 4 years, 8 months ago

CBSE > Class 10 > Social Science

1 answers

Poonguzhali.M Poonguzhali.M 4 years, 8 months ago

(i) Agriculture is the mainstay of Indian economy because about 60% of our population depends directly or indirectly on agriculture. (ii) It provides raw materials to the industries. (iii) India earns foreign exchange by exporting agricultural products. (iv) It contributes about 29% to the Gross Domestic Product.

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How water being a covalent compound show the properties of ionic compound??and why is water even a covalent compound

Posted by Ramesh Gupta 4 years, 8 months ago

CBSE > Class 10 > Science

2 answers

Bipin Kumar 4 years, 8 months ago

I didn't get your question

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Aryan Dev 4 years, 8 months ago

It is unique, it also has no confirm place in periodic table also, think it was a exception

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Sin × cos

Posted by Kanchan Singh 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Madhav Dixit 4 years, 8 months ago

sincos

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Mind map on the lesson A triumph of surgery. ( Class 10)

Posted by Deepa Dodamani 4 years, 8 months ago

CBSE > Class 10 > English Language and Literature

4 answers

Deepa Dodamani 4 years, 8 months ago

Ya please

3Thank You

Deepa Dodamani 4 years, 8 months ago

Yes please

3Thank You

Rana Name 1 year, 10 months ago

A TRIUMPH OF SURGERY By James Herriot  James Herriot stops his car and sees the poor health of Mrs Pumphrey’s dog, Tricki.  He advises Mrs Pumphrey to put Tricki on a strict diet and make him exercise daily.  Mrs Pumphrey continues to overfeed Tricki, which worsens his condition.  She calls Herriot for help on noticing Tricki’s deteriorating health.  Herriot decides to hospitalise Tricki for a fortnight to treat him.  Tricki’s hospitalisation left Mrs Pumphrey and the helpers at home in tears.  Tricki was kept on a strict diet in the hospital. His diet was increased according to the improvements he showed.  Mrs Pumphrey’s anxiousness about Tricki’s health went away on learning that Tricki was convalescing satisfactorily.  She started to send eggs, wine and brandy for Tricki to enrich his blood and improve his health.  These items were instead enjoyed by James Herriot and his partner.  Tricki was transformed from a weak fat dog to a hard-muscled and agile one.  James Herriot calls Mrs Pumphrey to come and take Tricki home 1. “Herriot is dutiful doctor who cared for other’s emotions more than his personal interests.” Prove the statement. 2. Do you think there are also parents like Mrs Pumphery? Give reasons for your answer.

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Bipin Kumar 1 year, 10 months ago

Can I provide it?

3Thank You

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Why does baking soda doesn't contain water of crystallisation?

Posted by Ramesh Gupta 4 years, 8 months ago

CBSE > Class 10 > Science

3 answers

Adithya Dev A 4 years, 8 months ago

Because it is partially soluble in water.

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Bipin Kumar 4 years, 8 months ago

Yes, obviously it's chemical formula doesn't contain water, as it is only upto 10

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Kavya Chanana 4 years, 8 months ago

Because its chemical formula does not contain Water of crystallisation

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You are Amit/Amita, a resident of Prem Vihar Colony, Aligarh, Uttar Pradesh. You have noticed that your next door neighbour family (all three members) have COVID-19 flu symptoms like persistent high fever along with cough and cold for more than a week. They are alternately flouting quarantine rules and despite repeated requests made by other neighbours, they are not getting themselves COVID- tested. Write a letter to the Medical Officer of the local hospital/dispensary, drawing attention towards the same. Explain how such acts impact the health of the community and request immediate intervention and strict action.

Posted by Sid Zirwal 4 years, 8 months ago

CBSE > Class 10 > English Language and Literature

0 answers

ANSWER

Why is diffusion insufficient to meet the oxygen required

Posted by Ankita Vijay 4 years, 8 months ago

CBSE > Class 10 > Science

2 answers

Ramesh Gupta 4 years, 8 months ago

If you are talking about human body,then perhaps I can answer it Human body is much larger and more complex in body structure then any other unicellular oragnism ,even if diffusion would take place it will take more than enough time to reach every cell of our body Thus diffusion is not sufficient for a large and complex organism

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Vansh Kamboj 4 years, 8 months ago

Hi ankita, how are you ❤ I am new here

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PART B-40 Marks Writing (10 marks) The insanitary conditions in your colony are causing multiple diseases. Write a letter in 100 -120 words to the Municipal commissioner bringing the problem to his notice and request him to take urgent action in the matter. You are Deepak / Deepa of C 2/8 Ankur Enclave, New Delhi. (5) OR You are Rajesh Ranjani of 105 C. Chaterjeee Lane, Kolkata. You have received a letter from your brother who is studying in the hostel of Shakti Mandir Public School. Darjeeling, stating that he is being bullied by some senior students who threatened him with dire consequences, if he complains. Write a letter in 100-120 words to the Hostel Warden requesting him to take urgent action 9 Colours play a very important role in our life. They have a healing power also. Read the table given below and use it to write an analytical paragraph on "Colour Therapy You are Shruti / Sharad of BPS Public School (5) COLOURS BENEFITS 1. GREEN Supports Balance, Harmony, Love, Communication, Social Nature. Acceptance 2. BLUE- INDIGO Increases Calmness, Love, Honesty. Kindness, Truth, Inner Peace, Emotional Depth, Devotion 3. VIOLET 4. RED 5. ORANGE 6. YELLOW Stimulates Intuition, Imagination, Universal Flow, Meditation Artistic qualities Increases Physical Energy, Vitality, Stamina, Spontaneity. Stability, Passion Stimulates Creativity, Productivity. Pleasure, Optimism. Enthusiasm, Emotional expression. Increases Fun, Humour, Lightness, Personal Power, Intellect, Logic, Creativity. OR Due to Covid -19 pundemic, all schools are closed and to mitigate the academic loss, online classes are being provided by the government and the schools. In this situation the role of cell phones, once prohibited in schools, now has become an essential need of the students. Write a paragraph in 100 -120 words on the topic "Importance of cell phones for the students during pandemic Covid -19" (5) 25

Posted by Karthick S 4 years, 8 months ago

CBSE > Class 10 > English Language and Literature

2 answers

Sia ? 4 years, 8 months ago

105 C, Chatterjee Lane,
Kolkata

Date: 06.11.2020

To
The Hostel Warden
Shakti Mandir Public School,
Darjeeling

Sub: Requesting to take urgent action on the issue of bullying

Sir,

I am Rajni Roy, sister of Paresh Biswas who is a student of Shakti Mandir Public School.
I have received a letter from my brother who is staying in your hostel. He conveyed that he is being bullied by some senior students who threatened him with dire consequences if he complained. I request you to take proper action on it.
I would be obliged if you consider the situation and take a step against this.

Yours faithfully,
Ranjani

3Thank You

Sia ? 4 years, 8 months ago

C 2/8, Ankur Enclave
New Delhi.

15 August 2020

The Municipal Commissioner
Municipal Office
New Delhi

Subject: Strict action against the insanitary conditions in the colony which can cause diseases.

Respected Madam/Sir

I am a resident of the the address given above. I would like to draw your kind attention to the unsanitary conditions in my colony, the trespassers just throw garbage here and there because there is no dustbin. The water of the drain is coming to the roads and giving it an unpleasant smell , mosquitoes are breeding in the water and flies roam around the garbage, which is also very unhygienic.
When we complained to head of the cleaning department , they said that the cleaners haven't been coming to work for many days and neither do they do their work sincerely.
In these conditions there is a chance of getting multiple diseases which also threatens the life of the residents. I request you to take some strict actions against it.
We would be grateful, if you could help.

Yours sincerely
Deepak/Deepa

6Thank You

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How is silk fibre produced?

Posted by Gulfiza Naaz 4 years, 8 months ago

CBSE > Class 10 > Social Science

3 answers

Krish Agrawal 4 years, 8 months ago

By killing the silkworms in hot water

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Aksa Merlin Thomas 4 years, 8 months ago

Silk fiber is produced by rearing silkworm and that process is called sericulture.

1Thank You

Deepa Dodamani 4 years, 8 months ago

From the silk worm

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Discribe what do you mean by nation state

Posted by Alfia Biju 4 years, 8 months ago

CBSE > Class 10 > Social Science

2 answers

Kalyani Shahi 4 years, 8 months ago

In nation state the citizens and the rulers shared a common identity and history after the ruler and common people have struggles........ ?

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Rana Name 4 years, 8 months ago

People belong to same culture and same language get to gether is called a nation state

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Which tool will you use in calc to make an estimate of output values for different input values? 1. Multiple operations 2. Macros 3. Scenarios 4. Goal seek Only 1 and 3 b) only 2 and 4 c)1,3 and 4 d) All of the given

Posted by Bhavya Sharma 4 years, 8 months ago

CBSE > Class 10 > Information Technology (402)

3 answers

Manish Kathayat 4 years, 8 months ago

Option a) 1 and 3

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Dashing Memes 4 years, 8 months ago

1 and 3 only

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Yashi . 4 years, 8 months ago

a)only 1 and 3

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alankar kise khte hai ??????

Posted by Mukhil Sharma 4 years, 8 months ago

CBSE > Class 10 > हिंदी ए

1 answers

Bhumi Sandeep Mande 4 years, 8 months ago

Alankar vo shabd hote hai jo kisi kaavyansh ki shobha badhaate hai.

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Write two uses of aluminium foil

Posted by Sayori Mukherjee 4 years, 8 months ago

CBSE > Class 10 > Science

2 answers

Muskan Kumari 4 years, 8 months ago

It is used for packing food

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X Y 4 years, 8 months ago

It is used for packing the food so that the food doesn't get rancid. It is also used to decorate food items. I'm not sure about the answers

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How does desire led to hatred? question from fire and ice

Posted by Shresth Kumar 4 years, 8 months ago

CBSE > Class 10 > English Language and Literature

1 answers

Kirti Deshwal 4 years, 8 months ago

Here Fire refers to desire And ice refers to the hatered

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As we move inlands towards the river valleys ,soil particles appear somewhat bigger in size . In the upper reaches of the river valley i.e. near the place of the break of the slope ,the soils are coarse . Such soils are more common in Piedmont Plains such as duars ,chos and terai.. Please explain in your own words..... By the way this?? is from lesson resources and development...

Posted by Harshu The Great 4 years, 8 months ago

CBSE > Class 10 > Social Science

0 answers

ANSWER

Chapter 1 questions answer

Posted by Ayush Pal 4 years, 8 months ago

CBSE > Class 10 > English Language and Literature

1 answers

Rana Name 4 years, 8 months ago

1. Whom did Lencho write a letter? What did he ask for and why? 2. What were Lencho's feelings when he found the letter with money in it? What did he do after opening it? 3. Why does the postmaster send money to Lencho? Why does he sign the letter 'God'? 4. What are the raindrops compared to and why? 5. Who does Lencho think has taken the rest of the money? Describe the ironical ending of the story?

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Cofficient of X+1

Posted by Tanisha Tanisha 4 years, 8 months ago

CBSE > Class 10 > Mathematics