FC: Semester 1 Geometry Exam Project By: Jacob Morton 2nd Period 12/12/11
1: Table of Contents | 3 topics/definitions From 1.1-1.5.... 2 Definition of angles and their measures.... 4 Definition of angle and segment bisector.... 6 Definition of complementary, supplementary, and vertical angles.... 6 Definition of parallel lines, and angles formed by transversal.... 10 Definition of Perpendicular lines.... 12 Definition of Triangles, angle measures.... 14 Definition of Pythagorean theorem and distance formula.... 16 Definition of Congruent Triangles.... 18 Definition of Polygons(parallelogram, rhombus, square, etc.).... 20
2: SECTIONS 1.1-1.5 | Point-has no dimension. It is represented by a small dot. | Line-has one dimension and extends without ending in two direction. It is represented by a line with two arrows. | Real World example- different points on the map form a sector in a city.
3: Plane-has two dimensions. It is represented by a shape that looks like a floor or wall. You have to imagine that it extends without end. Even though the drawing is only a certain size. | Real World example- on this virtual tennis court the lines form the rectangular shape and the different boxes that the players can stand in. | Real World example- this building model is made up of a plane to plot exact points of where a structure will go.
4: Definition of Angles and Their Measures | Right Angle- an angle with a 90 degree measure. | Acute Angle- an angle with a measure under 90 degrees. | Real World example- each corner of the build is made of a right angle. | Real World example- the section of the bridge where the cables connect is acute
5: Obtuse Angle- an angle with a measure over 90 degrees. | Real World example- many rooftops of old builds have a pattern in them, and the corners make obtuse angles.
6: Definition of Angle and Segment Bisectors | Angle Bisector- a ray that divides an angle into two angles that are congruent. | Real World example- angle bisectors are commonly seen in crossing railroad tracks and on the dial of a microwave.
7: Segment Bisector- a segment, ray, line, or plane that intersects a segment at its midpoint. | Real World example- segment bisectors can commonly be seen on maps depicting where a river or other landforms could be intersecting a line.
8: Definition of complementary, supplementary, and vertical angles | Complementary Angles- two angles whose measures have a sum of 90 degrees. | Real World example- many modern skyscrapers are built to have complementary angles. | Supplementary Angles- two angles whose sum has a measure of 180 degrees.
9: Real World example- many modern apartment and office building have been built with complementary angles. | Vertical Angles- two angles that are not adjacent and whose sides are formed by two intersecting lines. | Real World example- Older style buildings used vertical angles inside the structure to keep it stable.
10: Definition of parallel lines, angles formed by transversal | Parallel Lines- two lines that lie in the same plane and do not intersect. Real World example- train tracks are parallel since they do not touch at any point. | Alternate Interior angles- two angles that are formed between the two lines on opposite sides of the transversal. Real World example- these angles can be seen when a tree falls and bisects two other trees.
11: Alternate Exterior angles- two angles that are formed by two lines and a transversal, and lie on the outside. Real World example- Many different have maps lines that bisect and often form transversal and exterior angles. | Corresponding Angles- two angles that are formed by two lines and a transversal, and occupy corresponding positions. | Real World example- the landing gears of most commercial jets have corresponding landing gears.
12: Perpendicular Lines- two lines that intersect to form a right angle.
13: Real World example- sidewalk tiles laid next to each other form perpendicular lines.
14: Definition of Triangles and angle measures | Triangle- a figure formed by three segments joining three noncollinear points, called vertices. | Real World example- triangles are used in some road safety signs. | Right Triangle- a triangle with one right angle. | Real World example- right angles are commonly used in designing certain room styles or ceiling angles.
15: Scalene Triangle- a triangle with no congruent sides. | Real World example- scalene triangles can be seen from angles looking at certain buildings. | Obtuse Triangle- a triangle with one obtuse angle | Real World example- some rooftops are formed as obtuse angles.
16: Pythagorean Theorem and Distance Formula | Pythagorean Theorem- a2+b2+c2 | Real World example- the angle of a ladder against the wall.
17: Distance Formula- if A(x1,y1) and B(x2,y2) are points in a coordinate plane then the distance between A and B. | Real World example- the distance from the first floor to the fourth floor.
18: Definition of Congruent Triangles | 1. ASA 2. SAS 3. SSS 4. HL 5. AAS
19: Real World example- the shapes within the buildings are congruent triangles.
20: Definition of Polygons | Polygon- a plane figure that is formed by three or more segments called sides. Each side intersects exactly two other sides at each of its endpoints. | Rhombus- a parallelogram with four congruent sides. | Square- a parallelogram with four congruent sides and angles. | Rectangle- parallelogram with four congruent angles but congruent opposite sides.
21: Quadrilateral- a polygon with four sides.