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Transcript
VOCABULARY Chapters 1, 2, 3, 4, 5, 9, and 8 WORD Acute angle IMAGE • Acute triangle DEFINITION An angle with measure between 0° and 90° 56 A triangle with three acute angles. 60 50 70 Adjacent angles 1 2 Alternate interior angles Two angles in a plane that have a common vertex and a common side but no common interior points. ∠1 and ∠2 are adjacent angles Two nonadjacent interior angles on opposite sides of the transversal. *When 2 parallel lines are cut by a transversal, alternate interior angles are congruent. The perpendicular segment from a vertex to the line containing the opposite side. Altitude of a triangle Angle • A figure formed by two rays that have the same endpoint. Angle of Depression The angle formed by a horizontal line and a line of sight to a point below. Angle of Elevation The angle formed by a horizontal line and a line of sight to a point above. Biconditional Statement A statement that contains the words “if and only if.” Angle bisector A ray that divides the angle into two congruent adjacent angles. If ⃗⃗⃗⃗⃗⃗ 𝐵𝐷 bisects ∠ABC, then ∠1 ≅ ∠2. Centroid The point of concurrency of the three medians of a triangle. It is known as the center of gravity. Circumcenter Collinear points Complementary angles The point of concurrency of the three perpendicular bisectors of a triangle. It is the center of the circumscribed circle around a triangle. • 30° Points all in one line. • • Two angles whose measures have a sum of 90°. 60° Conclusion A statement whose basic form is If p, then q. “ q” is the conclusion. Conditional Statement A statement in the form “if –then.” The basic form of a conditional statement is “If p, then q.” Congruent angles Angles with equal measurement Congruent polygons Figures that have the same size and shape. Congruent segments Segments that have equal lengths. Converse The statement formed by switching the hypothesis and conclusion of a conditional statement: If q, then p. Coplanar points Points all in one plane. Corresponding angles Two angles in corresponding positions relative to two lines. *When 2 parallel lines are cut by a transversal, corresponding angles are congruent. Cosine In a right triangle, the ratio of the length of the leg adjacent the angle to the length of hypotenuse. cos = Adj. Hyp. Counterexample Deductive reasoning Ex. If an animal is a bird, then it can fly. Counterexample: A penguin is a bird, but cannot fly. Therefore, a “penguin” is a counterexample. Solving a proof is an example of using deductive reasoning. An example used to prove that an if-then statement is false. Proving statements by reasoning from accepted postulates, definitions, theorems, and given information. Dilation A transformation that preserves angle measure and results in an image with lengths proportional to the pre-image lengths. Example: Changing a smaller image into a bigger image. Equiangular triangle A triangle with all angles congruent. Equidistant The same distance from two or more objects. Equilateral triangle A triangle with three congruent sides. Exterior angle of a triangle ExteriorAngle The angle formed when one side of the triangle is extended. Hypotenuse The longest side of a right triangle located across from the right angle. Hypothesis A statement whose basic form is If p, then q. Statement p is the hypothesis. Image Each point P in a given set is mapped to exactly one point P’ in the same or a different set. P’ is called the image of P. Incenter Inductive reasoning Isosceles triangle The point of concurrency of the three angle bisectors of a triangle. A pop quiz is given the first three Fridays of the school year, so you conclude their will be a pop quiz every Friday. A kind of reasoning in which the conclusion is based on several past observations. A triangle with at least two sides congruent. Legs of an isosceles triangle The two congruent sides. Legs of a right triangle The two sides that create the right angle. Length of a segment The distance between its endpoints. Line A geometric figure which extends in two directions without ending. It has infinite points and no thickness. A pair of adjacent angles whose noncommon sides are opposite rays. Linear Pair Median of a triangle A segment from a vertex to the midpoint of the opposite side in a triangle. Midsegment of a triangle The segment that joins the midpoint of two sides of a triangle. Midpoint The point that divides a segment into two congruent segments. Non-collinear points Points not all in one line. Non-coplanar points Points not all in one plane. Obtuse angle An angle with measure between 90° and 180°. Obtuse triangle A triangle with one obtuse angle. Opposite rays Rays that have the same endpoint and go in opposite directions. Orthocenter The point of concurrency of the three altitudes of a triangle. Parallel lines Coplanar lines that do not intersect. Parallel planes Planes that do not intersect. Perpendicular bisector of a segment A line, segment, ray, or plane that is perpendicular to the segment at its midpoint. Perpendicular lines Two lines that intersect to form right or 90˚ angles. Plane NOT DEFINED, only described: Extends without ending and has no thickness and no edges. We usually picture a plane by drawing a four-sided figure. NOT DEFINED, only described: A dot that doesn’t have size, but does have some size. Point Points of Concurrency A point where three or more lines coincide. Polygon Postulate A closed plane figure formed by three or more segments such that each segment interacts exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear. EX. Angle Addition Postulate : Little Angle + Little Angle = Big Angle A statement that is accepted without proof. Pythagorean Theorem In a right triangle, the sum of the squares of the legs is equal to the sum of the square of the hypotenuse. Quadrilateral A four sided polygon. Ray Starts at an endpoint and goes in any direction without ending. Reflection A transformation in which a line of reflection acts like a mirror, reflecting points to their images. Remote Interior Angles An interior angle of a polygon that is not adjacent to the exterior angle. Right angle An angle with measure of 90°. Right triangle A triangle with one right angle. Rotation A transformation that turns a figure about a fixed point a number of degrees. Same-side interior angles Two interior angles on the same side of the transversal. *When 2 parallel lines are cut by a transversal, same side interior angles are supplementary. Scalene triangle A triangle with no congruent sides. Segment of a line Two points on the line and all points between them. Segment bisector A line, segment, ray, or plane that intersects a segment at its midpoint. Sine In a right triangle, the ratio of the length of the leg opposite the angle to the length of hypotenuse. SOH sin = Opp. Hyp. Skew Lines Lines that are not coplanar and do not intersect. Straight angle An angle measure of 180°. Supplementary angles Two angles whose measures have the sum of 180°. Tangent In a right triangle, the ratio of the length of the leg opposite the angle to the length of the leg adjacent. tan = opp adj TOA Theorem EX. Vertical Angle Theorem: Vertical Angles are congruent. A statement that has been proven. Transformation A change in position, size, or shape of a figure. Translation A transformation that moves every point in the figure the same distance in the same direction. Transversal A line that intersects two or more coplanar lines in different points. Triangle A figure formed by three segments joining three noncollinear points. Vertex of an angle The common endpoint in an angle. Vertex of a triangle Each of the three points of the triangle. 120 Vertical angles The nonadjacent angles formed by two intersecting lines.