FC: Ian's Geometry Scrapbook | By Ian Campbell 3 period 12/12/11
1: Table of Contents | Geometry basics .............................. 2 and 3 | Topic | Angle and Segment bisectors..................6 and 7 | Page number | Angles and there measure.................... 4 and 5 | Complementary, Supplementary, and Vertical angles.............................8 and 9 | Parallel lines and angles form by transversal's................................10 and 11 | Perpendicular lines........................... 12 and 13 | Triangles....................................... 14 and 15 | Pythagorean theorem an distance formula..............................16 and 17 | Congruent triangles..........................18 and 19 | Polygons.......................................20 and 21
2: Pattern-things that are arranged following a rule or rules. | Intersection-The point or points that two or more figures have in common. | Postulates- statements that are accepted without further justification. | Line AB intersects line DC at point E.
3: Real world examples | A real world example of a pattern is a checkerboard. | A real world example of an intersection.
4: Acute- an angle with measure between 0 and 90 degrees. | Obtuse- an angle with measure between 90 and 180 degrees. | Right angle- angle with a measure of 90 degrees.
5: Real world examples | A real world example of a right angle is the inside of monkey bars. | A real world example of an acute angle is kitchen togs. | A real world example of an obtuse angle is the hands on a clock.
6: Segment Bisector- a segment, ray, line , or plane that intersects a segment at its midpoint. | Line LO is a bisector of Segment AB. | Angle bisector- a ray that divides an angle into two angles that are congruent. | Ray AB bisects angle CAD because it divides the angle into two congruent angles
7: A real world example of a angle bisector is a hang glider. | The glider is the angle and the person is the bisector. | Real world examples | A real world example of a segment bisector is longitude and latitude. | Latitude is the segment and longitude is the segment bisector.
8: Complementary angles- Two angles whose measures have a sum of 90 degrees. | Supplementary angles- Two angles whose measures have a sum of 180 degrees. | Vertical angles- two angles that are not adjacent and whose sides are formed by two intersecting lines. | Angle 1 and angle 3 are vertical angles Angle 2 and angle 4 are vertical angles
9: Real world examples | A real world example of vertical angles is a pair of skies laid one on top of the other. | A real world example of supplementary lines is tennis court lines. | A real world example of complementary angles are the hands on a clock
10: Parallel lines- two lines that lie in the same plane and do not intersect. | Transversal- a line that intersects two or more coplanar lines at different points. | The red line is the transversal. | This is an example of angles formed by transversal.
11: Real world examples | A real world example of a transversal is the center piece of a window. | A real world example of parallel lines are strings on a guitar.
12: Perpendicular lines- two lines that intersect to form a right angle. | Line perpendicular to a plane- a line that intersects a plane in a point and is perpendicular to every line in the plane that intersects it. | Line BC is perpendicular to plane L.
13: Real World Examples | This blanket design shows an example of perpendicular lines. | This sidewalk has lines that is an example of perpendicular lines.
14: Triangle- A figure formed by three segments joining three non collinear points, called a vertex. | Triangles can be classified by its sides. Ex: Equilateral triangle has 3 congruent sides, Isosceles triangle has at least 2 congruent sides, and Scalene has no congruent sides. | Example of isosceles triangle | A triangle can be classified by its angles. Ex: Equiangular has 3 congruent angles, Acute has 3 acute angles, obtuse has 1 obtuse angle, and right triangle has 1 right angle. | Example of obtuse triangle
15: Real world examples | This is an example of a right angle triangle on a wooden door. | This picture shows an example of two isosceles triangles | Triangle sum Theorem- the sum of measures of the angles of a triangle is 180 degrees
16: Pythagorean Theorem- in a triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. | Distance formula- If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the distance between A and B is | Example of distance formula-
17: Real world examples | Some times you might need to use the Pythagorean when you are looking at map. | Often times when looking at a grid you will need to use the distance formula so you can find the distance between two points not on the same grid line.
18: SSS congruence- If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. | SAS congruence-If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. | ASA congruence-If two angles and the included side of one triangle are congruent to two angles and the included side of the second triangle, then the two triangles are congruent.
19: AAS congruence- If two angles and a non-included side of one triangle are congruent to two angles and the the corresponding non included side of a second triangle, then the two triangles are congruent. | HL congruence- if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. | Real world examples | HL | SAS
20: Polygons- are plane figures that are formed by three or more segments called sides. | parallelogram- is a quadrilateral with both pairs of opposite sides parallel. | Rhombus-a parallelogram with four congruent sides. | Rectangle- a parallelogram with four right angles.
21: Square- is a parallelogram with four congruent sides and four right angles. | Real world examples | The shapes on the pillow are examples of a rhombus. | These pans are a good example of rectangles. | The sides of a Rubik's cube is an example of a square.