BC: The End((:
FC: Geometry Project | By:Katie Missey 2nd Period 12/12/11
1: Table of Contents | Chapter 1.1-1.5...................................page 2 & 3 Angles and their measures......................page 4 & 5 Angle and Segment Bisectors...................page 6 & 7 Comp., Supp., Vertical Angles.................page 8 & 9 Parallel Lines and Transversal...............page 10 & 11 Perpendicular Lines...........................page 12 & 13 Triangles, Angle Measures....................page 14 &15 Pythagorean Theorem and Distance........page 16 & 17 Congruent Triangles...........................page 18 & 19 Polygons/Shapes...............................page 20 & 21
2: point: no dimension, a line has one dimension, and a plane has two dimensions. segment AB: consists of t endpoints A and B, and all points on line AB that are between A and B ray AB: consists of the endpoint A and all points on line AB that lie on the same side of A as B | right angle: 90 degrees obtuse angle: between 90-180 degrees. straight angle: 180 degrees. acute angle: between 0-90 degrees.
3: intersection: two or more figures is the point or points that the figures have in common. angle: consists of two rays that have the same endpoint. the rays are the sides of the angle. the endpoint is the vertex of the angle. measure: an angle is written in units called degrees.
4: angle: consists of two rays that have the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle. | angles and their measures
5: measure: an angle is written in units called degrees | Real World Example!
6: Angle Bisector-- | Real World Example: If you are looking at a brick wall, the crack of two bricks bisects the two bricks under or above them.
7: Segment Bisector-- a segment, ray, line, or plane that intersects a segment at its midpoint.
8: complementary angles: two angles that the sum of their measures is 90 degrees. each angle is the complement of the other. | vertical angles: if two angles are not adjacent and their sides are formed by two intersecting lines.
9: supplementary angles: two angles that the sum of their measures is 180. each angle is supplement of the other. | Real World Example(:
10: parallel lines: lie in the same plane but do NOT intersect. written as r//s. | transversal: a line that intersects two or more coplanar lines at different points
11: Angles Formed By a Transversal | -same side interior angles: if two angles lie between the two lines on the same side of the transversal. -alternate interior angles: two angles that lie between the two lines on the opposite sides of the transversal -alternate exterior angles: two angles that lie outside the two lines on the opposite sides of the transversal. -corresponding angles: if two angles occupy corresponding positions | 1 and 5, 2 and 6, 3 and 7, 4 and 8 are corresponding angles 3 and 6, 4 and 5 are alternate interior angles 1 and 8, 2 and 7 are alternate exterior angles 4 and 6, 3 and 5 are same side interior angles
12: perpendicular lines: intersect to form a right angle.
13: A real world example would be the lines on a tennis court. the middle line cuts the other line like perpendicular lines.
14: exterior angles of a triangle: the angles that are adjacent to the interior angles interior angles of a triangle: the three original angles when the sides of a triangle are extended base angles: two angles at the base of the isosceles triangle median of a triangle: a segment from a vertex to the midpoint of the opposite side. centroid of a triangle: the point where all three medians of the triangle intersect.
15: Real World Example
16: Pythagorean Theorem: in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
17: Distance Formula: if A(x1,y1) and B(x2,y2) are points in a coordinate plane. | Real World example: if you are to lean a ladder up against the wall you could use the Pythagorean Theorem to find out how far away from the wall you need to place the ladder.
18: Congruent Triangles | SSS- if 3 sides of one triangle are congruent to 3 sides of the second triangle then the triangles are congruent | SAS- if 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of a second triangle, then the triangle are congruent | AAS- if 2 angles and a non-included side of one triangle are congruent to two angle and the correspoding non- included side of a second triangle, then the two triangles are congruent. | ASA- if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. | HL- if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the two triangles are congruent.
19: SAS | SSS | AAS | ASA | HL
20: quadrilateral: 4 sides. pentagon: 5 sides. hexagon: 6 sides. heptagon: 7 sides. octagon: 8 sides. | parallelogram: if a quadrilateral is a parallelogram then both pairs of opposite sides are parallel. | trapezoid: quadrilateral with exactly one pair of parallel sides. isosceles trapezoid: if the legs of a trapezoid are congruent.
21: Polygon: a plane figure that is formed by three or more segments called sides | rhombus: four congruent sides rectangle: four RIGHT angles square: four congruent sides and four RIGHT angles | there are all kinds of signs that are shapes in cities/towns