Similarity

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The ratio of areas of two triangles = (Base₁ × Height₁)/(Base₂ × Height₂) If triangle ABC has base b₁ and height h₁, and triangle PQR has base b₂ and height h₂, then: A(△ABC)/A(△PQR) = (b₁ × h₁)/(b₂

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When two triangles have equal heights, the ratio of their areas equals the ratio of their corresponding bases. A(△ABC)/A(△PQR) = Base₁/Base₂ This is because the height cancels out in the formula: (b

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If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the same proportion. In △ABC, if line l ∥ BC and intersects AB at

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If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. In △ABC, if line PQ intersects AB and AC such that AP/PB = AQ/QC, then PQ ∥ BC.

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The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides. In △ABC, if the bisector of ∠C intersects AB at point D, then: AD/DB = CA/CB

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The ratio of the intercepts made on a transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same parallel lines. If lines l ∥

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Two triangles are similar if: 1. Their corresponding angles are equal 2. Their corresponding sides are proportional If △ABC and △DEF are similar, we write: △ABC ∼ △DEF This means: ∠A = ∠D, ∠B = ∠E,

Answer

AAA Test (Angle-Angle-Angle): For a given correspondence of vertices, when corresponding angles of two triangles are congruent, then the two triangles are similar. In △ABC and △PQR, if ∠A ≅ ∠P, ∠B ≅