WGU C972 College Geometry 100% Correct

WGU C972 College Geometry 100% Correct Area of a Circle A=πr² Arc Length Formula L = 2πr (m⁰/360⁰) Circumference of a circle 2πr or πd Area of a sector Area of a Sector = (central angle/360) x πr² Midpoint formula (x₁+x₂)/2, (y₁+y₂)/2 Distance Formula d = √[( x₂ - x₁)² + (y₂ - y₁)²] slope-intercept form y=mx+b point-slope form y - y1 = m(x - x1) intercept form x/a + y/b = 1 general form Ax + By + C = 0 definition of a tetrahedron closed solid structure formed by a set of planes; has 4 sides and is a triangular pyramid definition of a octahedron 3-d shaped polyhedron with 8 faces sum of interior angles of a polygon (n-2)180 supplementary angles Two angles whose sum is 180 degrees vertical angles two nonadjacent angles formed by two intersecting lines and their measurements are congruent complimentary angles two angles that add up to 90 degrees linear pair of angles two angles that share a vertex, a common side, and their non-common sides form a line. angle bisector a ray that divides an angle into two congruent angles adjacent angles Two angles that share a common side and have the same vertex 45-45-90 triangle x, x, x√2 30-60-90 triangle 1:√3:2 area of a triangle A= 1/2 bh Perimeter of a polygon sum of the lengths of the sides Angle Addition Postulate for any angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts Corresponding Angles Postulate If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. alternate exterior angles theorem If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then same-side interior angles are supplementary. and their sums equal 180 degrees obtuse angle An angle that measures more than 90 degrees but less than 180 degrees acute angle an angle that measures less than 90 degrees scalene triangle a triangle with no congruent sides isosceles triangle a triangle with at least two congruent sides equilateral triangle A triangle with three congruent sides polygon A closed plane figure made up of line segments regular polygon a polygon that is both equilateral and equiangular irregular polygon a polygon with sides that are not all congruent or angles that are not all congruent concave if any part of a diagonal contains points in the exterior of the polygon(ie..star shape) convex if no diagonal contains points in the exterior (ie. a regular polygon) Polygon Exterior Angle Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. Circle (definition) the set of all points in a plane that are equidistant from a common fixed point (the center) by a distance (radius), joined together to form a closed figure triangle median line segment joining a midpoint of one side to its opposite vertex triangle altitude line segment through a vertex and is perpendicular to the opposite side of the triangle. orthocenter of a triangle the point of concurrency of the three altitudes of a triangle Triangle Midsegment Theorem A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side. Every triangle has 3 midsegments, which form the midsegment triangle. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180 degrees Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. 3rd angle theorem If 2 angles of a triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. perpendicular bisector A line that is perpendicular to a segment at its midpoint. (creates 2 equal parts) angle bisector a ray that divides an angle into two congruent angles Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle circumcenter of a triangle the point of concurrency (intersection) of the perpendicular bisectors of a triangle; it is equidistant from the vertices of that triangle circumscribed circle a circle with an inscribed polygon( ie..a triangle inside of a circle) incenter of a triangle the point of concurrency of the angle bisectors of a triangle inscribed circle A circle that is inside a triangle and is tangent to its sides. medians and angle bisectors always meet inside a triangle centroid of a triangle The point of concurrency of the medians of a triangle; it is located 2/3'rds of the distance from each vertex to the midpoint of the opposite side. Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. Pythagorean triple Set of 3 nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem Area of 30-60-90 Triangle A=sqrt of 3/2(s squared) Area of 45-45-90 triangle 1/2 (a squared) Area of equilateral triangle A=(s²√3)/4 area of 30-30-120 triangle A=1/2bh SAS Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are similar. ASA Theorem If two angles and the included side of one triangle are equal to two angles and the included side of another triangle then the triangles are congruent AAS if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent SSS Similarity Theorem If the corresponding 3 side lengths of two triangles are proportional, then the triangles are similar. Hypotenuse Leg Theorem 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. corresponding parts of congruent triangles are congruent CPCTC Every plane has an equation that can be written as Ax + By + Cz + D =0 Parallelogram A quadrilateral with two pairs of parallel sides rectangle A parallelogram with four right angles Rhombus A parallelogram with four congruent sides square A parallelogram with four congruent sides and four right angles. It is a rectangle and a rhombus. Standard form of the equation of a circle (x-h)^2 + (y-k)^2 = r^2 Ellipse set of all points, P, in a plane, the sum of whose distances form 2 fixed (foci) points, F1 and F2, is constant. standard form for the equation of an ellipse; starting point Center @ (0,0) horizontal ellipse equation x^2/a^2 + y^2/b^2 = 1, where a is greater than or equal to b vertical ellipse equation y^2/a^2 + x^2/b^2 = 1, where a is greater than or equal to b. Length of the major axis of an ellipse 2a length of minor axis (ellipse) 2b Volume of a Sphere Formula V=4/3πr³ Volume of a Cone Formula V=1/3πr²h Volume of a rectangular pyramid 1/3 lwh Volume of a Cylinder Formula V=πr²h or V=Bh Volume of a rectangular prism V=lwh volume of a polygon prism V=Bh Volume of a cube formula V=s^3 Surface area of a rectangular prism SA=2lw+2lh+2wh function a mapping from a set A domain the set of allowable inputs Distance Preserving if the distance between the images of 2 points is always equal to the distance between the pre images of the 2 points onto function each element of the range corresponds to an element of the domain one-to-one function a function where each element of the range is paired with exactly one element of the domain translation type of isometry where an input point is moved or dragged to a new location by translation; nothing changes during the move. It is a rigid movement from one place to another. glide reflection The transformation that is a combination of a reflection and a translation that is across a parallel line to the translation vector. composition of transformations one transformation followed by another isometry A transformation in which the preimage and image are congruent rotation If you do a reflection across 2 intersecting lines, it is equivocal to a(n) reflections Any translation or rotation is equivalent to a composition of two 3 types of isometries reflection, rotation, and translation Transformation a function that changes the position, shape, and/or size of a figure Transformation a function that is both one-to-one and onto Dilation A transformation that changes the size of an object, but not the shape.