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Mathematics 217

Chapters 11 - 12

TermDefinition
Line A line has no thickness and it extends forever in two directions.
Line segment A subset of a line that contains two points of the line and all points between those two points.
Ray A subset of the line AB that contains the endpoint A, the point B, all points between A and B, and all points C on the line such that B is between A and C.
Skew line Lines GF and DE are skew lines. They do not intersect, and there is no plane that contains them.
Concurrent line Lines DE, EG, and EF are concurrent lines; they intersect at point E.
Parallel line Line m is parallel to line n. They have no points in common.
Axiom Axioms are statements that cannot be proven and are assumed.
Theorem Theorems are statements that can be proven using axioms and logic.
Half plane Line AB separates plane "a" into two half-planes.
Angle An angle is formed by two rays with the same endpoint.
Vertex Vertex is the common endpoint of the two rays that form an angle.
Sides of an angle The sides of an angle are the two rays that form an angle.
Adjacent angle Adjacent angles are two angles with a common vertex and a common side, but without overlapping interiors.
Radian An angle of 1 radian is an angle whose vertex is at the center of a circle and that intercepts an arc equal in length to the radius of the circle. 1 radian ≈ 57.296 degrees
A line perpendicular to a plane A line perpendicular to a plane is a line that is perpendicular to every line in the plane through its intersection with the plane.
Dihedral angle A dihedral angle is formed by the union of two half-planes and the common line defining the half-planes.
Dimensional analysis (or unit analysis) Dimensional analysis (or unit analysis) is a process to convert from one unit of measurement to another.
Triangle inequality theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. AB + BC > AC
Perimeter Perimeter is the length of a simple closed curve, or the sum of the lengths of the sides of a polygon.
Circle Circle is the set of all points in a plane that are the same distance from a given point, the center.
Circumference Circumference is the perimeter of a circle.
Pi Pi is the ratio between the circumference of a circle and the length of its diameter.
Simple curve Simple curve is a curve that does not cross itself; starting and stopping points may be the same.
Closed curve Closed curve is a curve that starts and stops at the same point.
Polygon A polygon is a simple, closed curve with sides that are line segments.
Convex curve Convex curve is a simple, closed curve with no indentations; the segment connecting any two points in the interior of the curve is wholly contained in the interior of the curve.
Concave curve Concave curve is a simple, closed curve that is not convex; it has an indentation.
Interior angle Interior angle is an angle formed by two sides of a polygon with a common vertex.
Diagonal Diagonal is a line segment connecting nonconsecutive vertices of a polygon.
Exterior angle of a convex polygon Exterior angle of a convex polygon is an angle formed by a side of a polygon and the extension of a contiguous side of the polygon.
Congruent part Congruent parts are parts with the same size and shape.
Regular polygon If all sides of a polygon are congruent and all angles are congruent, the polygon is a regular polygon. A regular polygon is equilateral and equiangular.
Right triangle Right triangle is a triangle containing a right angle.
Acute triangle Acute triangle is a triangle in which all the angles are acute.
Obtuse triangle Obtuse triangle is a triangle containing an obtuse angle.
Scale triangle Scalene triangle is a triangle with no congruent sides.
Isoceles triangle Isosceles triangle is a triangle with at least two congruent sides.
Equilateral triangle Equilateral triangle is a triangle with three congruent sides.
Trapezoid Trapezoid is a quadrilateral with at least one pair of parallel sides.
Kite Kite is a quadrilateral with two adjacent sides congruent and the other two sides also congruent.
Isoceles trapezoid Isoceles trapezoid is a trapezoid with congruent base angles.
Parallelogram Parallelogram is a quadrilateral in which each pair of opposite sides is parallel.
Rectangle Rectangle is a parallelogram with a right angle.
Rhombus Rhombus is a parallelogram with two adjacent sides congruent.
Square Square is a rectangle with two adjacent sides congruent.
Line of symmetry Mathematically, a geometric figure has a line of symmetry ℓ if it is its own image under a reflection in ℓ.
Rotational (turn) symmetry A figure has rotational symmetry, or turn symmetry, when the traced figure can be rotated less than 360° about some point, the turn center, so that it matches the original figure.
Point symmetry Any figure that has rotational symmetry 180° is said to have point symmetry about the turn center.
Vertical angle Vertical angles are created by intersecting lines are a pair of angles whose sides are two pairs of opposite rays.
Supplementary angle The sum of the measures of two supplementary angles is 180°.
Complementary angle The sum of the measures of two complementary angles is 90°.
Transversal and angle Angles formed when a line (a transversal) intersects two distinct lines.
Angle and parallel line property If any two distinct coplanar lines are cut by a transversal, then a pair of corresponding angles, alternate interior angles, or alternate exterior angles are congruent if, and only if, the lines are parallel.
The sum of the measures of the interior angles of a triangle Since the angles appear to form a straight angle, we conjecture that the angles sum up to 180 degrees.
The sum of the measures of the exterior angles of a convex n - gon The sum of the measures of the exterior angles of a convex n - gon is 360 degrees.
Similar object Similar objects have the same shape but not necessarily the same size.
Congruent object Congruent objects have the same shape and the same size.
Arc An arc of a circle is any part of the circle that can be drawn without lifting a pencil.
Center of an arc The center of an arc is the center of the circle containing the arc.
Semicircle If the two arcs determined by a pair of points on the circle are the same size, each is a semicircle.
Chord A segment connecting two points on a circle is a chord of the circle.
Diameter If a chord contains the center, it is a diameter.
Triangle congruence Two figures are congruent if it is possible to fit one figure onto the other so that matching parts coincide.
Side, side, side congruence condition (SSS) If the three sides of one triangle are congruent, respectively, to the three sides of a second triangle, then the triangles are congruent.
Side, angle, side property (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, respectively, then the two triangles are congruent.
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.
Altitude An altitude of a triangle is the perpendicular segment from a vertex of the triangle to the line containing the opposite side of the triangle.
Angle, Side, Angle (ASA) property If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, respectively, then the triangles are congruent.
Angle, angle, side (AAS) If two angles and a side opposite one of these two angles of a triangle are congruent to the two corresponding angles and the corresponding side in another triangle, then the two triangles are congruent.
Properties of angle bisectors Any point P on an angle bisector is equidistant from the sides of the angle. same. Any point that is equidistant from the sides of an angle is on the angle bisector of the angle.
Incenter of a triangle The angle bisectors of a triangle are concurrent (they intersect in a single point, the incenter) and the three distances from the point of intersection to the sides are equal.
Similar polygon Two polygons with the same number of vertices are similar if there is a one-to-one correspondence between the vertices of one and the vertices.
AA similarity for triangle If two angles of one triangle are congruent, respectively, to two angles of a second triangle, then the triangles are similar.
SSS similarity for triangle If corresponding sides of two triangles are proportional, then the triangles are similar.
SAS similarity for triangle Given two triangles, if two sides are proportional and the included angles are congruent, then the triangles are similar.
Properties of proportion If a line parallel to one side of a triangle intersects the other sides, then it divides those sides into proportional segments.
Properties of proportion If parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on any transversal.
Midsegment of triangles and quadrilaterals The midsegment (segment connecting the midpoints of two sides of a triangle) is parallel to the third side of the triangle and half as long.
Median A median of a triangle is a segment connecting a vertex of the triangle to the midpoint of the opposite side.
Center of gravity or centroid The three medians are concurrent. The point of intersection, G, is the center of gravity, or the centroid, of the triangle.
Indirect measurement Similar triangles have long been used to make indirect measurements.
Created by: marianhood