# Theorems pythagorean inequality theorem the

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Theorems: Pythagorean inequality theorem: The Pythagorean inequality is a generalization of the Pythagorean theorem, which states that in a right triangle with sides of length we have The inequality says: For an acute triangle with sides of length For an obtuse triangle with sides. Week 16:45-45-90 Special right triangle: type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.30-60-90 Special triangle: a special right triangle (a right triangle being any triangle thatcontains a 90 degree angle) that always has degree angles of 30 degrees, 60 degrees, and 90 degrees.Sin0= opposite---------- HypotenuseTan 0= opposite------------Adjacent-Finding an unknown angle= An unknown angle problem is a puzzle consisting of a figure with the measures of some sides and angles given and with one angle — the unknown angle — marked with a letter.-Angle of elevation: The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye-Angle of depression: The angle which slowly increases downQuick facts 4-16 are included in both glossary and formula,All postulates, theorems, and corollaries. Week 17: -A diagonal: To joining two opposite corners of a square, rectangle, or other straight-sided
shape.-Triangle - Sum of angles 180 degrees: A straight line falling on parallel straight lines makes alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles. -Quadrilateral: Four sided figure-Pentagon: a plane figure with five straight sides and five angles.-Hexagon: a plane figure with six straight sides and angles.-Polygon interior angle sum theorem: Polygon interior angles sum theorem. The sum of the measures of the interior angles of a convex polygon with n sides is. -Polygon exterior sum theorems: If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° . Consider the sum of the measures ofthe exterior angles for an n -gon.-Parallelogram: a four-sided plane rectilinear figure with opposite sides parallel.-Theorem: Properties of parallelograms: If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram. THEOREM: If a quadrilateral has consecutive angles are supplementary, then it is a parallelogram.-Theorem: Diagonals of parallelogram: If a quadrilateral has diagonals that bisect each other, then it is a parallelogram. Theorem: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram. Week 18:Theroems: Conditions for parallelogram: If a quadrilateral has consecutive angles are supplementary, then it is a parallelogram. If a quadrilateral has diagonals which bisect each other, then it is a parallelogram.
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