* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download File
Survey
Document related concepts
Problem of Apollonius wikipedia , lookup
Dessin d'enfant wikipedia , lookup
Lie sphere geometry wikipedia , lookup
Multilateration wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Euler angles wikipedia , lookup
Perceived visual angle wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Line (geometry) wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Transcript
Guided Notes for Lesson 1.1 Three building blocks of geometry are . A , , and is the most basic building block. It has no size, only . A is a straight, continuous arrangement of infinitely many points. It has indefinite but no . A has length and width, but no . It is like a flat surface that extends along its length and width. A is a statement that clarifies or explains the meaning of a word or a phrase. means on the same line. means on the same plane. A consists of two points called the of the segment and all between them are collinear with the two . Two segments are segments if and only if they have the same measure or length. The of a segment is the point on the segment that is the same distance from both . The midpoint the segment, or divides the segment into two segments. A begins at a point and extends infinitely in one direction. Guided Notes for Lesson 1.2 An is formed by two rays that share a common endpoint, provided the two rays are noncollinear. The common endpoint is the of the angle. The two rays are the of the angle. The is the smallest amount of about the vertex from one ray to the other, measured in . It can be any value between 0° and 180°. The geometry tool used to measure an angle is a Two angles are same measure. A ray is the divides the angle into two . angles if and only if they have the if it contains the vertex and angles. Guided Notes for Lesson 1.3 A is an example that contradicts a definition. Beginning steps to creating a good definition 1. your term. 2. your term. 3. your definition by looking for a counterexample. Two lines that do not intersect and are non-coplanar are lines. A angle is an angle that measures 90°. An angle is an angle that measure less than 90°. An angle is an angle that measure more than 90° but less than 180°. angles are angles formed by two intersecting lines; they share a common vertex, but not a common side. Two angles are a if they share a common side and their non-common sides form a A pair of angles has a sum of 90°. A pair of angles has a sum of 180°. and a . Guided Notes for Lesson 1.4 A is a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. Each endpoint where the sides meet is called a polygon. You classify a polygon by the number of A of a polygon is a line non-consecutive vertices. of the is has. that connects two A polygon is if no diagonal is outside the polygon. A polygon is polygon. if at least one diagonal is outside the Two polygons are exactly the same size and polygons if and only if they are . In an , all the sides have equal length. In an , all angles have equal measure. A is both equilateral and equiangular. Guided Notes for Lesson 1.5 To something is to accept it as true without facts or proof. A triangle has one right angle. An triangle has three An triangle has one obtuse angle. A triangle is a triangle with no congruent sides. An triangle has three congruent sides. An triangle has at least two congruent sides. angles. In an isosceles triangle, the angle between the two sides of equal length is called the angle. The side opposite the the isosceles triangle. angle is called the of The two angles opposite the two sides of equal length are called the of the isosceles triangle. A is a quadrilateral with exactly one pair of parallel sides. A is a quadrilateral with two distinct consecutive congruent sides. A sides. A A of is a quadrilateral with two pairs of is an equilateral parallelogram. is a parallelogram with four angles. A and a is an equilateral rectangle, an quadrilateral. rhombus, Guided Notes for Lesson 1.6 A is the set of all points in a plane at a given distance (radius) from a given point (center) in the plane. A segment from the center to appoint on the edge of the circle is called a . The is a line segment containing the center with its on the circle. If two or more circles have the same radius, they are circles. If two or more coplanar circles share the same center, they are . An of a is two points on the circle and the continuous part of the circle between the two points, which are called . A is an arc of a circle whose endpoints are the endpoints of a diameter. A semicircle. is an arc of a circle that is smaller than a A semicircle. is an arc of a circle that is larger than a You find the arc measure by measuring the , which is the angle with its vertex at the of the circle and sides passing through the endpoints of the arc. A is a line segment whose endpoints lie on the circle. A is a chord that passes through the chord. and is the A is a line that intersects the circle only once. The point where this line touches the circle is called the of . Guided Notes for Lessons 1.7 and 1.8 Sometimes there is more than one point (or even many points) that satisfy a set of conditions. The set of points is called a of points. is the set of all points. It cannot be contained in a flat surface.