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किस विधि के अनुसार, दो त्रिभुज समान होते हैं यदि उनके दोनों भुजाओं और एक गैर-समावेशित भुजा समान होते हैं?
क्या एक त्रिभुज के दोनों समकोण और एक समावेशित भुजा, एक और त्रिभुज के दोनों कोणों और एक न समावेशित भुजा के समान होने पर, त्रिभुज समान होते हैं?
त्रिभुज समान होने की प्रमुख विधि क्या है?
हेक्टर-हेक्टर (HH) समांतरता किसे कहलाती है?
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पूर्विक-समांतरता (SSS) समांतरता में क्या महत्वपूर्ण है?
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दो त्रिभुज SSS समानता के लिए क्या शर्त है?
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SAS समानता क्या दिखाती है?
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क्या ASA समानता SAS समानता से ज्यादा संबंधित है?
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साइड-साइड-साइड (SSS) के मुताबिक, दो त्रिभुज कैसे माप-सरहित होते हैं?
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क्या SAS समानता SSS समानता में पूरक है?
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Study Notes
Triangle Congruence
Triangles are fundamental shapes in geometry, and their properties can help us understand when two triangles are equivalent or congruent. When two triangles are congruent, it means they share the same shape and size. In this article, we'll delve into some of the most common ways to determine if triangles are congruent.
Side-Side-Side (SSS) Congruence
When three corresponding sides of two triangles are equal in length, the triangles are congruent. This is called Side-Side-Side (SSS) Congruence. The equality of sides implies that the triangles share the same scale factor, making them identical copies of each other.
Side-Angle-Side (SAS) Congruence
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. This is called Side-Angle-Side (SAS) Congruence. This condition allows us to relate the lengths of sides to the sizes of their included angles.
Angle-Side-Angle (ASA) Congruence
When two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. This is called Angle-Side-Angle (ASA) Congruence. This condition is more complex than SAS because it relates the sizes of angles to the lengths of sides.
Angle-Angle-Side (AAS) Congruence
If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, the triangles are congruent. This is called Angle-Angle-Side (AAS) Congruence. This condition is more abstract than ASA because it does not necessarily relate the lengths of sides to the sizes of their included angles.
Hypotenuse-Leg (HL) Congruence
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent. This is called Hypotenuse-Leg (HL) Congruence. This condition allows us to determine when two right triangles are congruent without resorting to their interior angles.
Triangle Congruence Theorem
The Triangle Congruence Theorem states that if two triangles are congruent in any one of the above-mentioned ways, then they must be congruent in all six ways. This theorem is essential because it provides a systematic way to check for triangle congruence.
Summary
Understanding triangle congruence is essential for geometric reasoning, as it helps us understand when two triangles are equivalent and, consequently, when we can apply properties of one triangle to another. This topic is fundamental in geometry and is used in calculating area, volumes, and solving problems in various fields, such as architecture and engineering.
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Description
इस आलेख में हम त्रिभुज की समानता को समझने के लिए विभिन्न तरीकों पर ध्यान केंद्रित करेंगे, जैसे साइड-साइड-साइड, साइड-कोन-साइड, कोण-साइड-कोण, और हाइपोटेनूस-लेग. हम भी त्रिभुज समानता के प्रमुख सिद्धांत को समझेंगे।
