AFOQT Latest 2023 with Certified Solutions

AFOQT Latest 2023 with Certified Solutions Triangle 3 internal angles add to 180, 3 sided Angle Bisector extends from one side to BISECT the opposing angle Triangle altitude the shortest distace from a vertex angle to the side containing the base Triangle Median extends from one angle to BISECT the opposite side Two centers of a triangle Centroid or orthocenter Centroid Where the triangles 3 medians meet Orthocenter where the triangles 3 altitudes meet Scalene triangle no equal sides of angles Isosceles Has 2 equal sides and 2 equal angles often called base angles Equilateral Triangle All 3 sides and angles are equal 60 degrees Rigth triangle Has one right angle 90 and two acute angles Acute triangle all 3 angles less than 90 Obtuse 2 acute and one angle greater then 90 Triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side Third-side rule of triangles three sides, a, b, c. c-b < a < c+b Pythagorean Theorem The relatioship between the sides of a right triangle is a2 + b2 = c2 (all squared) where c is the hypotenuse and is across from the right angle. Right triangle with angle measurements 90-45-45 Special right triangle. the hypotenuse is equal to the square root of 2x Right triangle with angle measurments 90-60-30 Special right enuse is 2x. the short side is x and the long side is square root of 3x Quadrilaterals A closed, 4 sided shape. The sum of all 4 sides is always equal to 360. The AREA of quadrilateral is always A= bh (base time height) Parallelogram A quadrilateral with two pairs of equal side. Two consecutive sides in a parallelogram are supplementary = 180 Rectangle two pairs of equal sides and four right angles Kite two pairs of equal sides but the equal sides are consecutive Square 4 right angles and 4 equal sides Rhombus 4 equal sides. diagonals bisects angles and bisect one another Trapezoid One pair of sides is parallel bases have different lengths Polygons Any closed shape made up of 3 or more line segments. Hexagon = 6, Octagon = 8 The sum of all exterior angles in a polygon is 360 Finding the sum of the interior angles of polygons (n-2) x 180 where n is the number of sides the polygon has. To find a single interior angle simply divide the total interior angles by the # of sides and therefor angles Apothem the shortest PERPENDICULAR distance from one of the sides to the center Area of Polygon A = ap/2 (apothem x perimeter) finding an interior angle of a polygon (n-2)/n x 180 Area of Circle A = PieRsquared Volume