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24 Cards in this Set

  • Front
  • Back
Congruent Polgons
have congruent corresponding parts (sides and angles) When you name them you must list corresponding vertices in the same order
Third Angle Theorem (theorem 4-1)
If two angles are congruent to two angles of another triangle, then the third angles are congruent.
Side-Side-Side (sss) Postulate (Postulate 4-1)
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Postulate (Postulate 4-2)
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
Angle-Side_Angle (ASA) Postulate (postulate 4-3)
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.
Angle-Angle-Sie (AAS) theorem (theorem 4-2)
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.
Isoceles Triangle
a triangle that has at two congruent sides (two sides are equal in length)
Equalateral triangle
a triangle with three congruent sides (all sides are equal in length)
Scalene Traingle
a triangle with no congruent sides (all sides have different lengths)
leg (isosceles triangle)
congruent sides of an isosceles triangle
vertex (isoceles triangle)
in an isosceles triangle the angle formed between two congruent legs
base (isocceles trianlge)
the third side of an isosceles triangle (the non-congruent side)
base angle (isosceles trianlge)
_____ the angles in an isosceles triangle that are not the vertex (the two angles touching the base)
Isoceles triangle theorem (theorem 4-3)
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Converse of the Isoceles triangle theorem (theorem 4-4)
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Theorem 4-5
If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base.
corollary
a theorem that can be proved easily using another theorem
Corollary to the Isosceles triangle Theorem (theorem 4-3)
If a triangle is equilateral, then the triangle is equiangular
Corollary to the converse of the isosceles triangle theorem (theorem 4-4)
If a triangle is equangular, then the triangle is equilateral
right triangle
a triangle containing a right (90 degree) angle
leg (right triangle)
the two shorter sides of a right triangle (the two sides touching the right angle)
hypotenuse
the longest side of a right triangle (it is opposite the right angle)
Hypotenue-Leg (HL) Theorem (Theorem 4-6)
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.
Pythagorean Theorem
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