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Class 9 8.2 is about mid point theorem It says .. In a triangle, the line segment that joins the mid point of any two sides is parallel to the third side also half of it

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Show that diagonals of a square that quadrilateral PQRS is a rhombus

Posted by Charu Singh 2 years, 11 months ago

CBSE > Class 09 > Mathematics

1 answers

Preeti Dabral 2 years, 11 months ago

Given: Let ABCD is a quadrilateral.
Let its diagonal AC and BD bisect each other at right angle at point O.

{tex}\therefore {/tex}OA = OC, OB = OD
And {tex}\angle {/tex}AOB = {tex}\angle {/tex}BOC = {tex}\angle {/tex}COD = {tex}\angle {/tex}AOD = {tex}{90^ \circ }{/tex}
To prove: ABCD is a rhombus.
Proof: In {tex}\triangle{/tex}AOD and {tex}\triangle{/tex} BOC,
OA = OC [Given]
{tex}\angle {/tex}AOD = {tex}\angle {/tex}BOC [Given]
OB = OD [Given]
{tex}\therefore {/tex} {tex}\triangle{/tex}AOD {tex} \cong{/tex} {tex}\triangle{/tex}COB [By SAS congruency]
{tex} \Rightarrow {/tex} AD = CB [By C.P.C.T.]……….(i)
Again, In {tex}\triangle{/tex}AOB and {tex}\triangle{/tex}COD,
OA = OC [Given]
{tex}\angle {/tex} AOB = {tex}\angle {/tex}COD [Given]
OB = OD [Given]
{tex}\therefore {/tex} {tex}\triangle{/tex}AOB {tex} \cong {/tex} {tex}\triangle{/tex}COD [By SAS congruency]
{tex} \Rightarrow {/tex} AB = CD [By C.P.C.T.]……….(ii)
Now In {tex}\triangle{/tex}AOB and {tex}\triangle{/tex}BOC,
OA = OC [Given]
{tex}\angle {/tex} AOB = {tex}\angle {/tex}BOC [Given]
OB = OB [Common]
{tex}\therefore {/tex} {tex}\triangle{/tex}AOB {tex} \cong{/tex} {tex}\triangle{/tex}COB [By SAS congruency]
{tex} \Rightarrow {/tex} AB = BC [By C.P.C.T.]……….(iii)
From eq. (i), (ii) and (iii),
AD = BC = CD = AB
And the diagonals of quadrilateral ABCD bisect each other at right angle.
Therefore, ABCD is a rhombus.

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At some moment, two giant planets Jupiter and Saturn of the solar system are in the same line as seen from the earth. Find the total gravitational force due to them on a person of mass 50 kg on the earth. Could the force due to the planets be important? Mass of the Jupiter = 2 × 1027 kg Mass of the Saturn = 6 × 1026 kg The distance of Jupiter from the earth = 6.3 × 1011 m The distance of Saturn from the earth = 1.28 × 1012 m A bag of sugar weighs ‘w’ at a certain place on the equator. If this bag is taken to Antarctica, then will it weigh the same or more or less. Give a reason for your answer.

Posted by Sehajpreet Kaur 3 years ago

CBSE > Class 09 > Science

1 answers

Sehajpreet Kaur 3 years ago

In Δ ABC, P and Q are the mid-points of sides AB and BC respectively. ∴ PQ || AC and PQ = 12 AC ( Using mid-point theorem) …..(1) In ΔADC, R and S are the mid - points of CD and AD respectively. ∴ RS || AC and RS = 12 AC ( Using mid-point theorem) …..(2) From equation (1) and (2) , we obtain PQ || RS and PQ = RS Since in quadrilateral PQRs, one pair of opposite sides is equal and parallel to each other , it is a parallelogram. Let the diagonals of rhombus ABCD intersect each other at point O. In Quadrilateral OMQN, MQ || ON (∵ PQ || AC) QN || OM (∵ QR || BD) Therefore, OMQN is a parallelogram. ∴∠MQN=∠NOM and ∠PQR=∠NOM However, ∠NOM=90∘ (Diagonals of a rhombus are perpendicular to each other) ∴∠PQR=90∘ Clearly , PQRS is a parallelogram having one of its interior angles as 90∘ Hence, PQRS is a rectangle.

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A circular path with center A mathav walk at uniform speed of 0.5 m/s from gate p and reach the center of park in 150 sec what is the streat distance between the center of the path and gate M

Posted by Jaini Gandhi 3 years ago

CBSE > Class 09 > Mathematics

1 answers

Akshadeep Meshram 3 years ago

75m

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Scientific forest

Posted by Ronak Verma 3 years ago

CBSE > Class 09 > Social Science

2 answers

Debayan Kar 3 years ago

In history ch5

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Ronak Verma 3 years ago

Scientific forest

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BBC compacta Beehive prose Extracts Solution

Posted by Sakshi Deswal 3 years ago

CBSE > Class 09 > English Lang & Lit. (184)

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Which of these are the pastrol communities of Africa

Posted by Veer Singh 3 years ago

CBSE > Class 09 > Social Science

2 answers

Tanveer Kaur 3 years ago

Bedouins .berbers. massai .Somali. turkana.

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Debayan Kar 3 years ago

Maasai

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A sample of pure water, irrespective of its source contains 11.1% hydrogen and 88.9% oxygen. The data support

Posted by Konthoujam _Malemnganbii_Chanu Chanuu 3 years ago

CBSE > Class 09 > Science

2 answers

Smriti Gupta 2 years, 11 months ago

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Harsh Soni 3 years ago

Tha answer is 2

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The value of 50- root 32×root50 is

Posted by Bhavani S. K 3 years ago

CBSE > Class 09 > Mathematics

2 answers

Debayan Kar 3 years ago

50-√32×√50 =50-4√2×5√2 =50-20×√2×√2 =50-20×2 =50-40 =10

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Akshadeep Meshram 3 years ago

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English me pass kaise hoi

Posted by Kavya Arun Rai 3 years ago

CBSE > Class 09 > English Lang & Lit. (184)

4 answers

Aditya Maurya 2 years, 11 months ago

Ese bakwas karke

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Rudranshi Thakur 3 years ago

Padhai karke

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Debayan Kar 3 years ago

Practice any CBSE sample paper

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Girija Devi Pati 3 years ago

padhke

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ABCD is a rhombus and P,Q,R,S are the mid point of the sides AB,BC,CD,DA respectively. Show that the quadrilateral PQRS is a rectangle .

Posted by Sasmita Mallick 3 years ago

CBSE > Class 09 > Mathematics

1 answers

Sehajpreet Kaur 3 years ago

In Δ ABC, P and Q are the mid-points of sides AB and BC respectively. ∴ PQ || AC and PQ = 1 2 AC ( Using mid-point theorem) …..(1) In Δ ADC, R and S are the mid - points of CD and AD respectively. ∴ RS || AC and RS = 1 2 AC ( Using mid-point theorem) …..(2) From equation (1) and (2) , we obtain PQ || RS and PQ = RS Since in quadrilateral PQRs, one pair of opposite sides is equal and parallel to each other , it is a parallelogram. Let the diagonals of rhombus ABCD intersect each other at point O. In Quadrilateral OMQN, MQ || ON ( ∵ PQ || AC) QN || OM ( ∵ QR || BD) Therefore, OMQN is a parallelogram. ∴ ∠ M Q N = ∠ N O M and ∠ P Q R = ∠ N O M However, ∠ N O M = 90 ∘ (Diagonals of a rhombus are perpendicular to each other) ∴ ∠ P Q R = 90 ∘ Clearly , PQRS is a parallelogram having one of its interior angles as 90 ∘ Hence, PQRS is a rectangle.

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Factorise : √3x²+4x+3x

Posted by Riya Singh 3 years ago

CBSE > Class 09 > Mathematics

2 answers

Akshadeep Meshram 2 years, 11 months ago

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Mohak Yadav 3 years ago

Question is wrong

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Which irrational number does not lie between 2/7 & 3/5

Posted by Lavesh Sahu 3 years ago

CBSE > Class 09 > Mathematics

2 answers

Shivang Sharma 2 years, 11 months ago

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Lavesh Sahu 3 years ago

17/35

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Solve if you are intelligent! In triangle ABC, AD is the median. AC = 12cm, DC = 10cm, AD = 15cm. Find the length AB. Hint:- AD bisects the side BC

Posted by Akshadeep Meshram 3 years ago

CBSE > Class 09 > Mathematics

3 answers

Fatima Zafar 2 years, 11 months ago

Answer 5√13

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Akshadeep Meshram 3 years ago

Your answer is wrong aman kumar

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Aman Kumar 3 years ago

18cm

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Who called farm labourers

Posted by Swati Yadav 3 years ago

CBSE > Class 09 > Social Science

3 answers

Debayan Kar 3 years ago

Stop akshadeep

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Debayan Kar 3 years ago

In rural areas Farm laborers who could not buy land and necessary items which are daily needs for livelihood due to less income as more indebtedness

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Akshadeep Meshram 2 years, 11 months ago

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who holds the important portfolios like defence Finance home affairs etc and are generally the senior most minster? (a) speaker (b) ministers of state (c) deputy ministers (d) cabinet ministers

Posted by Bts Stan7 3 years ago

CBSE > Class 09 > Social Science

2 answers

Debayan Kar 3 years ago

C.deputy minsters

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Sumeet Singh 2 years, 11 months ago

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Find the average mass of isotopes CL³⁵(75%) and CL³⁷(25%)

Posted by Daksh Agarwal 3 years ago

CBSE > Class 09 > Science

3 answers

Smriti Gupta 2 years, 11 months ago

35.5 u

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Srishti Singh 3 years ago

For calculating this firstly u have to see it's mass number and percentage Formula- (Percentage×mass number/100) Calculation:- (75% × 35/100) + (25% × 37/100) =} (2625÷100)+(925÷100) =} (3550÷100) = 35.5u Answer :-. 35.5u *THANK YOU* 😊

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Akshadeep Meshram 3 years ago

Exam hone wala hai kya tera?

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What is title bar

Posted by Abhinandan Sahu 3 years ago

CBSE > Class 09 > Information Technology (402)

2 answers

Deepika Saini 3 years ago

Title bar just locate at the top of writer window. It contain the name of currently document which is opened

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Priyanshu Kumar 3 years ago

what do you mean by keyboarding skills

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आरक्षित निवचिन क्षेत्र से आप क्या समझते हैं?

Posted by Shivani Kashyap 3 years ago

CBSE > Class 09 > सामाजिक विज्ञान

2 answers

Kaif Alam 2 years, 5 months ago

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Vinay Yadav 3 years ago

Social science का sample paper class 9 का Answer

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पालमपुर में बिजली के प्रसार ने किसानों की किस तरह मदद की

Posted by Aaditya Arnav 3 years ago

CBSE > Class 09 > सामाजिक विज्ञान

1 answers

Lakshay Kumar 2 years, 11 months ago

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Plz sample paper

Posted by Sanjukta Borah 3 years ago

CBSE > Class 09 > Information Technology (402)

2 answers

ɢᴀᴜʀɪ Rajput 3 years ago

Just go to this link

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ɢᴀᴜʀɪ Rajput 3 years ago

https://drive.google.com/file/d/1tQ0igeXX1Qscpz6uhyHXxDkJ6ZdThN7O/view?usp=drivesdk

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Narendra wants to write y².but when he this , it shows y2 .Which option he should use to get 2 at proper place

Posted by Shubhangiba Rathod 3 years ago

CBSE > Class 09 > Information Technology (402)

3 answers

Swayam Pandey 2 years, 11 months ago

Superscript

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Atifa Riyaz 3 years ago

Superscript

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Devansh Yadav 3 years ago

Superscript

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assertion: fundamental rights are enforceable by any court. reason : the supreme court has the authority to issue directions, orders or writs for the enforcement of any fundamental right Option (A) and (R) both are true and (R) is the correct explanation of (A). (A) and (R) both are true, but (R) is not the correct explanation of (A). (A) is true, but (R) is false. (A) is false, but (R) is true.

Posted by Akanksha Shah 3 years ago

CBSE > Class 09 > Social Science

1 answers

Aaditya Kumar 3 years ago

A is fals but R is true

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Write difference between slide and presentation

Posted by Mohammad Saim 3 years ago

CBSE > Class 09 > Information Technology (402)

1 answers

Deepika Saini 3 years ago

Impress working area known as slide

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Different between prokaryotic

Posted by B. Wamsi 3 years ago

CBSE > Class 09 > Science

1 answers

B. Wamsi 3 years ago

Answer Kya ha

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Represent underroot 6 on number line

Posted by Anjali Mattu 3 years ago

CBSE > Class 09 > Mathematics

2 answers

Debayan Kar 3 years ago

1. Material required are ruler , notebook, pencil with compass and eraser

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Abhishek Ranjan 3 years ago

Plz give m answer

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How we get food?

Posted by Gauri Gauri 3 years ago

CBSE > Class 09 > Science

2 answers

Shivam Sharma 3 years ago

We get food from plants and animals

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Gauri Gauri 3 years ago

We get food from plants and animals

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Write down four important of chart is our daily life

Posted by Satyam Yadav 3 years ago

CBSE > Class 09 > Computer Applications (165)

2 answers

Shivam Sankpal 2 years, 11 months ago

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Kashvi Jain 3 years ago

Line chart Bar chart Pie chart Area chart

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How is LAN different from WAN

Posted by Bhupendra Chauhan 3 years ago

CBSE > Class 09 > Information Technology (402)