Theorems

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Theorems

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Theorem 9: if two sides of a triangle are equal, the angles opposite them are equal
Theorem 13: if two sides of a triangle are unequal, the angles opposite them are unequal in the same order
Theorem 27: a quadrilateral is a parallelogram if its opposite sides are equal
Theorem 57: if a line through the center of a circle bisects a chord that is not a diameter, it is also perpendicular to the chord
Theorem 5 (linear pairs): the angles in a linear pair are supplementary
Theorem 21: an exterior angle of a triangle is equal to the sum of the remote interior angles
Theorem 40: the area of a parallelogram is the product of any base and its corresponding altitude
Theorem 8 (linear pairs/perpendicular): if the angles in a linear pair are equal, then then their sides are perpendicular
SSS Similarity Theorem: if the sides of one triangle are proportional to the sides of another triangle, then the triangles are similar
Theorem 15 (triangle inequality): sum of any two sides of a triangle is greater than the third side
SAS Similarity Theorem: if an angle of one triangle is equal to an angle of another triangle and the sides including these angles are proportional, then the triangles are similar
Theorem 31: all rectangles are parallelograms
Theorem 41: the area of a trapezoid is half the product of its altitude and the sum of its bases
Theorem 25: the opposite sides and angles of a parallelogram are equal
Theorem 28: a quadrilateral is a parallelogram if its opposite angles are equal
Theorem 29: a quadrilateral is a parallelogram if two opposite sides are both parallel and equal
Theorem 3 (complements): complements of the same angle are equal
Theorem 7 (perpendicular lines): perpendicular lines form right angles
Theorem 37 (midsegment): a midsegment of a triangle is parallel to the third side and half as long
Theorem 56: if a line through the center of a circle is perpendicular to a chord, it also bisects the chord
Theorem 60: if a line is perpendicular to a radius at its outer endpoint, it is tangent to the circle
Theorem 20 (triangle angle sum): the sum of the angles of a triangle is 180 degrees
Theorem 2 (B.O.R.): if OA-OB-OC, then
Theorem 51: In a 30-60-90 triangle, the hypotenuse is twice the shorter leg and the longer leg is the square root of 3 times the shorter leg
Theorem 6 (vertical angles): vertical angles are equal
Theorem 24 (quadrilateral angle sum): the sum of the angles of a quadrilateral is 360 degrees
Theorem 43 (converse of pythagorean): if the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is a right triangle
Theorem 59: if a line is tangent to a circle, it its perpendicular to the radius drawn to the point of contact
Theorem 17: equal corresponding angles mean that lines are parallel
Theorem 16: in a plane, two points each equidistant from the endpoints of a line segment determine the perpendicular bisector of the line segment
Theorem 1 (B.O.P.): if A-B-C, then AB+BC=AC
Theorem 14: if two angles of a triangle are unequal, the sides opposite them are unequal in the same order
Theorem 10: if two angles of a triangle are equal, the sides opposite them are equal
Theorem 26: the diagonals of a parallelogram bisect each other
Theorem 36: the diagonals of an isosceles trapezoid are equal
Theorem 53: two nonvertical lines are perpendicular iff the product of their slopes is -1
Theorem 12 (exterior angle): an exterior angle of a triangle is greater than either remote interior angle
Theorem 42 (pythagorean): the square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs
Theorem 23 (hl): if the hypotenuse and a leg of one right triangle are equal to the corresponding parts of another right triangle, the triangles are congruent
Theorem 32: all rhombuses are parallelograms
Theorem 46: corresponding altitudes of similar triangles have the same ratio as that of the corresponding sides
Theorem 19: parallel lines form equal corresponding angles
Theorem 49: the altitude to the hypotenuse of the a right triangle forms two triangles similar to it and to each other
Theorem 52: two nonvertical lines are parallel iff their slopes are equal
Theorem 18: in a plane, two lines parallel to a third line are parallel to each other
Theorem 11 (sss): if the three side of one triangle are equal to three sides fo another triangle, the triangles are congruent
Theorem 55 (law of cosines): if the sides opposite
Theorem 4 (supplements): supplements of the same angle are equal
Theorem 54 (law of sines): if the sides opposite
Theorem 33: the diagonals of a rectangle are equal
Theorem 45 (aa): if two angles of one triangle are equal to two angles of another triangle, the triangles are similar
Theorem 35: the base angles of an isosceles trapezoid are equal
Theorem 30: a quadrilateral is a parallelogram if its diagonals bisect each other
Theorem 39: the area of a triangle is half the product of any base and its corresponding altitude
Theorem 34: the diagonals of a rhombus are perpendicular
Theorem 50 (Isosceles Right Triangle): in an isosceles right triangle, the hypotenuse is the square root of two times the length of a leg
Theorem 48: the ratio of the areas of two similar polygons is equal to the square of the ratio of the corresponding sides
Theorem 22 (aas): if two angles and the side opposite one of them in one triangle are equal to the corresponding parts of another right triangle, the triangles are congruent
Theorem 58: the perpendicular bisector of a chord of a circle contains the center of the circle
Theorem 44 (side splitter): if a line parallel to one side of a triangle intersects the other two sides in different points, it divides the sides in the same ratio
Theorem 47: the ratio of the perimeters of two similar polygons is equal to the ratio of the corresponding sides
Theorem 38: the area of a right triangle is half the product of its legs

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Number of cards 62