Triangles

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Congruent figures are figures that have the same shape and the same size. They can be placed on each other to cover completely. Examples: Two coins of same denomination, two bangles of same size, moul…

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Two triangles are congruent if all corresponding sides and all corresponding angles are equal. This means one triangle can be placed exactly over the other to cover it completely. We write △ABC ≅ △PQR…

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CPCT stands for 'Corresponding Parts of Congruent Triangles'. It means that if two triangles are congruent, then their corresponding sides are equal and their corresponding angles are equal.

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SAS (Side-Angle-Side) Congruence Rule: Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. The angl…

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ASA (Angle-Side-Angle) Congruence Rule: Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle. The side mu…

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AAS (Angle-Angle-Side) Congruence Rule: Two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal. This works because if two angles are equal, the third angl…

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Equality of three angles is not sufficient for congruence because triangles with same angles can have different sizes. For example, all triangles with angles 40°, 50°, and 90° are similar but not nece…

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An isosceles triangle is a triangle in which two sides are equal. Important property: In an isosceles triangle, the angles opposite to the equal sides are equal. If AB = AC, then ∠B = ∠C.