कोण-कोण समरूपता कसौटी - Revision history

Mani: added content

2024-09-23T11:39:54Z

added content

← Older revision		Revision as of 17:09, 23 September 2024
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	~~The Angle~~-~~Angle~~ (AA) ~~criterion for similarity of two triangles states that “If two angles of one triangle are respectively equal to two angles of another triangle~~, ~~then the two triangles are similar”.~~		दो त्रिभुजों की समरूपता के लिए कोण-कोण (AA) कसौटी/मानदंड बताता है कि "यदि एक त्रिभुज के दो कोण क्रमशः दूसरे त्रिभुज के दो कोणों के समान हैं, तो दोनों त्रिभुज समरूप हैं"।

	~~The~~ AA ~~criterion states that if two angles of a triangle are respectively equal to the two angles of another triangle~~, ~~we can prove that the third angle will also be equal on both the triangles. This can be done with the help of the angle sum property of a triangle.~~		AA कसौटी/मानदंड बताता है कि यदि एक त्रिभुज के दो कोण क्रमशः दूसरे त्रिभुज के दो कोणों के समान हैं, तो हम सिद्ध कर सकते हैं कि दोनों त्रिभुजों पर तीसरा कोण भी समान होगा। यह त्रिभुज के कोण योग गुण की मदद से किया जा सकता है।

	== ~~Example~~ ==		== उदाहरण ==
	1.~~Diagonals~~ <math>AC</math> ~~and~~ <math>BD</math> ~~of a trapezium~~ <math>ABCD</math> ~~with~~ <math>AB \parallel DC</math> ~~intersect each other at the point~~ <math>O</math>~~. Using a similarity criterion for two triangles, show that~~ <math>\frac{OA}{OC}=\frac{OB}{OD}</math>		1.विकर्णों <math>AC</math> और <math>BD</math> एक समलंब <math>ABCD</math>,जिसमें <math>AB \parallel DC</math> हो और एक दूसरे को बिंदु <math>O</math> पर प्रतिच्छेद करते हैं। दो त्रिभुजों के लिए समरूपता मानदंड का उपयोग करते हुए दर्शाइए कि <math>\frac{OA}{OC}=\frac{OB}{OD}</math>

	'''~~Solution~~:'''		'''हल:'''

	~~Let's draw a trapezium~~ <math>ABCD</math> ~~with~~ <math>AB \parallel DC</math>		आइए एक समलंब <math>ABCD</math> चतुर्भुज बनाते हैं जिसमें <math>AB \parallel DC</math> हो
	[[File:Example-4.jpg\|none\|thumb]]		[[File:Example-4.jpg\|none\|thumb]]
	~~If two angles of one triangle are respectively equal to two angles of another triangle~~, ~~then the two triangles are similar.~~		यदि एक त्रिभुज के दो कोण क्रमशः दूसरे त्रिभुज के दो कोणों के समान हों, तो दोनों त्रिभुज समरूप होते हैं।

	~~This is referred to as~~ AA ~~similarity criterion for two triangles.~~		इसे दो त्रिभुजों के लिए AA समरूपता मानदंड के रूप में जाना जाता है।

	In <math>\triangle AOB</math> and <math>\triangle COD</math>		In <math>\triangle AOB</math> and <math>\triangle COD</math>

	<math>\angle AOB =\angle COD</math> (~~vertically opposite angles~~)		<math>\angle AOB =\angle COD</math> (ऊर्ध्वाधर विपरीत कोण)

	<math>\angle BAO =\angle DCO</math> (~~alternate interior angles~~)		<math>\angle BAO =\angle DCO</math> (वैकल्पिक आंतरिक कोण)

	~~Hence~~ <math>\triangle AOB \sim \triangle COD</math> (AA ~~similarity criterion~~)		अत: <math>\triangle AOB \sim \triangle COD</math> (AA समरूपता कसौटी)

	~~Hence~~ <math>\frac{OA}{OC}=\frac{OB}{OD}</math>		अत: <math>\frac{OA}{OC}=\frac{OB}{OD}</math>

	[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]		[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]

Mani at 11:27, 23 September 2024

2024-09-23T11:27:37Z

← Older revision		Revision as of 16:57, 23 September 2024
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			The Angle-Angle (AA) criterion for similarity of two triangles states that “If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar”.

			The AA criterion states that if two angles of a triangle are respectively equal to the two angles of another triangle, we can prove that the third angle will also be equal on both the triangles. This can be done with the help of the angle sum property of a triangle.

			== Example ==
			1.Diagonals <math>AC</math> and <math>BD</math> of a trapezium <math>ABCD</math> with <math>AB \parallel DC</math> intersect each other at the point <math>O</math>. Using a similarity criterion for two triangles, show that <math>\frac{OA}{OC}=\frac{OB}{OD}</math>

			'''Solution:'''

			Let's draw a trapezium <math>ABCD</math> with <math>AB \parallel DC</math>
			[[File:Example-4.jpg\|none\|thumb]]
			If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

			This is referred to as AA similarity criterion for two triangles.

			In <math>\triangle AOB</math> and <math>\triangle COD</math>

			<math>\angle AOB =\angle COD</math> (vertically opposite angles)

			<math>\angle BAO =\angle DCO</math> (alternate interior angles)

			Hence <math>\triangle AOB \sim \triangle COD</math> (AA similarity criterion)

			Hence <math>\frac{OA}{OC}=\frac{OB}{OD}</math>

	[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]		[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]
	~~Angle-Angle similarity Criterion~~

Mani at 08:22, 23 August 2023

2023-08-23T08:22:45Z

← Older revision		Revision as of 13:52, 23 August 2023
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	[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]		[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]
			Angle-Angle similarity Criterion

Mani: Updated Category

2023-08-04T14:07:58Z

Updated Category

← Older revision		Revision as of 19:37, 4 August 2023
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	~~[[Category:ज्यामिति]]~~
	[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]		[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]

Sarika at 05:35, 4 August 2023

2023-08-04T05:35:35Z

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	[[Category:ज्यामिति]]		[[Category:ज्यामिति]]
	[[Category:त्रिभुज]][[Category:गणित]]		[[Category:त्रिभुज]][[Category:गणित]][[Category:कक्षा-10]]

Sarika at 05:31, 4 August 2023

2023-08-04T05:31:50Z

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	[[Category:ज्यामिति]]		[[Category:ज्यामिति]]
	[[Category:त्रिभुज]]		[[Category:त्रिभुज]][[Category:गणित]]

Sarika at 10:58, 18 April 2023

2023-04-18T10:58:17Z

← Older revision		Revision as of 16:28, 18 April 2023
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	~~[[Category:गणित]]~~
	[[Category:ज्यामिति]]		[[Category:ज्यामिति]]
	[[Category:त्रिभुज~~]][[Category: कक्षा-10~~]]		[[Category:त्रिभुज]]

Sarika at 06:42, 21 March 2023

2023-03-21T06:42:08Z

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	[[Category:गणित]]		[[Category:गणित]]
	[[Category:ज्यामिति]]		[[Category:ज्यामिति]]
	[[Category:त्रिभुज]]		[[Category:त्रिभुज]][[Category: कक्षा-10]]

Mani: added category

2023-01-25T12:07:37Z

added category

← Older revision		Revision as of 17:37, 25 January 2023
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	[[Category:ज्यामिति]]		[[Category:ज्यामिति]]
			[[Category:त्रिभुज]]

Mani: added category

2023-01-25T12:07:18Z

added category

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	[[Category:गणित]]		[[Category:गणित]]
			[[Category:ज्यामिति]]