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What is the first sign (criterion) for triangle congruence?
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The first sign is Side-Side-Side (SSS) criterion, where all three sides of one triangle are equal to the three sides of another triangle.
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What condition must be met for triangles to be congruent under the Side-Side-Side (SSS) criterion?
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All three corresponding sides of the triangles must be equal in length.
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How is the Side-Side-Angle (SSA) criterion different from the others for triangle congruence?
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SSA is not a valid congruence criterion as it can result in two different triangles.
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What is the second sign (criterion) for triangle congruence?
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The second sign is Angle-Side-Angle (ASA) criterion, where two angles and the side between them in one triangle are equal to the corresponding two angles and the side in another triangle.
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In the ASA criterion, which parts of the triangles must be known to prove congruence?
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Two angles and the included side of the triangles.
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Can triangles be congruent if only their angles are equal?
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No, angles alone cannot ensure congruence unless the sides are also proportional (similar triangles).
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Which side of a triangle is referred to as the 'included side' in the ASA criterion?
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The side that lies between the two given angles.
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How do the SSS and ASA criteria ensure triangles are identical in shape and size?
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They ensure that the triangles have corresponding equal sides and angles, making them identical.
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What is one real-life application of the triangle congruence criteria?
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Verifying the congruence of structures in construction to ensure parts fit together perfectly.
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Why isn't the SSA criterion considered valid for proving triangle congruence?
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Because it can lead to the creation of two different triangles with the same dimensions.
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In terms of triangle congruence, what do corresponding parts refer to?
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Corresponding parts are the sides and angles that are in the same relative position in different triangles.
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How does knowing two sides and the included angle help in the determination of triangle congruence?
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This is part of the Angle-Side-Angle (ASA) and Side-Angle-Side (SAS) criteria, which help to establish full congruence by equating the known sides and angle.
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What is another name for the ASA congruence criterion?
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It is also known as the Angle-Side-Angle postulate.
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How do geometrical proofs benefit from triangle congruence criteria?
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They provide essential logical tools for proving the equivalency of geometric shapes and structures.
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What role does educated guessing play in proving triangle congruence?
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Educated guessing (hypothesis) is used wisely to establish a starting point in proofs, but precise measurement and logical deduction confirm congruence.
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