Chapter 4 Postulates, Theorems, Corollaries, and Formulas – Flashcards
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Theorem 4.1 "Angle Sum Theorem" (HW Theorem 3-11)
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The sum of the measures of the angles of a triangle is 180.
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Theorem 4.2 "Third Angle Theorem" (HW Corollary 1)
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If 2 angles of one triangle are congruent to 2 angles of a second triangle, then the third angles of the triangles are congruent.
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HW Corollary 2
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Each angle of an equiangular triangle has a measure of 60.
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Corollary 4.1 (HW Corollary 4)
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The acute angles of a right triangle are complementary.
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HW Corollary 3
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There can be at most 1 right or obtuse angle in a triangle.
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Theorem 3.4 "Exterior Angle Theorem"
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 remote interior angles.
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Postulate 4-1 "SSS Postulate" (HW Postulate 12)
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If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
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Postulate 4-2 "SAS Postulate" (HW Postulate 13)
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If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
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Postulate 4-3 "ASA Postulate" (HW Postulate 14)
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If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
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Theorem 4.9 "Isosceles Triangle Theorem" (HW Theorem 4-1)
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If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
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Corollary 4.3 (HW Corollary 1)
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A triangle is equilateral if and only if it is equiangular.
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Corollary 4.4 (HW Corollary 2)
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Each angle of an equilateral triangle measures 60°.
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HW Corollary 3
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The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.
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Theorem 4.10 "Converse of the Isosceles Triangle Theorem" (HW Theorem 4-2)
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If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
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Theorem 4.5 "AAS Theorem" (HW Theorem 4-3)
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If two angles and the non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent
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"HL Theorem"
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If the hypotenuse and leg of one right triangle are congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.
