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24 Cards in this Set
- Front
- Back
Congruent Polgons
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have congruent corresponding parts (sides and angles) When you name them you must list corresponding vertices in the same order
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Third Angle Theorem (theorem 4-1)
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If two angles are congruent to two angles of another triangle, then the third angles are congruent.
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Side-Side-Side (sss) Postulate (Postulate 4-1)
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If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
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Side-Angle-Side (SAS) Postulate (Postulate 4-2)
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If two sides and the included angle of one triangle are congruent to two sides and the congruent angle of another triangle, then the two triangles are congruent
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Angle-Side_Angle (ASA) Postulate (postulate 4-3)
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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 two triangles are congruent.
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Angle-Angle-Sie (AAS) theorem (theorem 4-2)
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If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of one triangle, then the triangles are congruent.
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Isoceles Triangle
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a triangle that has at two congruent sides (two sides are equal in length)
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Equalateral triangle
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a triangle with three congruent sides (all sides are equal in length)
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Scalene Traingle
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a triangle with no congruent sides (all sides have different lengths)
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leg (isosceles triangle)
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congruent sides of an isosceles triangle
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vertex (isoceles triangle)
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in an isosceles triangle the angle formed between two congruent legs
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base (isocceles trianlge)
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the third side of an isosceles triangle (the non-congruent side)
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base angle (isosceles trianlge)
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_____ the angles in an isosceles triangle that are not the vertex (the two angles touching the base)
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Isoceles triangle theorem (theorem 4-3)
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If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
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Converse of the Isoceles triangle theorem (theorem 4-4)
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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
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If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base.
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corollary
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a theorem that can be proved easily using another theorem
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Corollary to the Isosceles triangle Theorem (theorem 4-3)
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If a triangle is equilateral, then the triangle is equiangular
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Corollary to the converse of the isosceles triangle theorem (theorem 4-4)
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If a triangle is equangular, then the triangle is equilateral
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right triangle
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a triangle containing a right (90 degree) angle
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leg (right triangle)
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the two shorter sides of a right triangle (the two sides touching the right angle)
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hypotenuse
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the longest side of a right triangle (it is opposite the right angle)
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Hypotenue-Leg (HL) Theorem (Theorem 4-6)
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If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
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Pythagorean Theorem
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a^2+b^2=c^2 when a and b are legs and c is the hypotenuse
Read: a squared pluse b squared equals c squared |