FC: Geometry Scrapbook | Shali Griffy 2nd Period 11-18-15
1: Table of Contents | Page1: Table of Contents Pages 2-3: Geometry Basics Pages 4-5: Angles and Their Measures Pages 6-7: Angle and Segment Bisectors Pages 8-9: Complementary, Supplementary, and Vertical Angles Pages 10-11: Parallel Lines and Angles formed by a Transversal Pages 12-13: Perpendicular Lines Pages 14-15: Triangles and Angle Measures Pages 16-17: Pythagorean Theorem and Distance Formula Pages 18-19: Congruent Triangles Pages 20-21: Polygons Pages 22-23: Geometric Terms | 1
2: Geometry Basics | 3. A conjecture is an unproven statement that is based on a pattern or observation. | 1. A point has no dimension. It is represented by a small dot. | 2. Figures intersect if they have any points in common. | 2
3: 3 | Real World Relation: Intersection
4: 4 | Angles and Their Measures | 1. An angle consists of two ray that have the same endpoint. | 2. Acute angles measure between 0-90 degrees. | 3. Right angles measure is 90 degrees. | 4. Obtuse angles measure between 90-180 degrees. | 5. Straight angles measure is 180 degrees.
5: 5 | Real World Relation: Obtuse Fan
6: 6 | 1. An angle bisector is a ray that divides an angle into two angles that are congruent. | 2. A segment bisector is a segment, ray, line, or plane that intersects a segment at it's midpoint. | Angle and Segment Bisectors
7: 7 | Real World Relation: Dart Board Angle Bisector
8: EGG | 8 | 1. Two angles are complementary angles if the sum of their measures is 90 degrees. | Complementary, Supplementary, and Vertical Angles | 2. Two angles are supplementary angles if the sum of their measures is 180 degrees. | 3. Two angles are vertical angles if they are not adjacent and their sides are formed by two intersecting lines.
9: 9 | Real World Relation: Scissors
10: 10 | Parallel Lines And Angles Formed By A Transversal | 1. Two lines that lie in the same plane and do not intersect are parallel lines. | 2. Two angles are corresponding angles if they occupy corresponding positions. | 3. Two angles are same side interior angles if they lie between the two lines on the same side of the transversal.
11: 11 | Real World Relation: Railroad Tracks | 4. Two angles are alternate exterior angles if they lie between the two lines on the opposite side of the transversal. | 5. Two angles are alternate interior angles if they lie between the two lines on the opposite sides of the transversal.
12: 12 | Perpendicular Lines | 1. Two lines are perpendicular lines if they intersect to form a right angle.
13: 13 | Real World Relation: Tile Flooring
14: 14 | Triangles And Angle Measures | 1. A triangle is a figure formed by three segments joining three noncollinear points. A triangle can be classified by it's sides and it's angles. | 2. An equilateral triangle has 3 congruent sides. | 3. An isosceles triangle has at least 2 congruent sides. | 4. A scalene triangle has no congruent sides.
15: 15 | 5. An equiangular triangle has 3 congruent angles. | 6. An acute triangle has 3 acute angles. | 7. A right triangle has 1 right angle. | 8. An obtuse triangle has 1 obtuse angle. | Real World Relation: Instrumental Triangle
16: 16 | 1. The Pythagorean Theorem: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the legs. | 2. The distance formula gives the distance between two points in a coordinate plane. | Pythagorean Theorem And Distance Formula
17: 17 | Real World Relation: Space Between The Binder And The Shelf
18: 18 | 1. Figures are congruent if all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent. | Congruent Triangles | 2. If 3 sides of one triangle are congruent to 3 sides of a 2nd triangle, then the two triangles are congruent. (SSS) | 3. If two sides and the included angle of 1 triangle are congruent to two sides and the included angle of a 2nd triangle, then the two triangles are congruent. (SAS)
19: 19 | 5. If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non- included side of a 2nd triangle, then the two triangles are congruent. (AAS) | 7. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a 2nd right triangle, then the two triangles are congruent. (HL) | 4. If two angles and the included side of one triangle are congruent to two angles and the included side of a 2nd triangle, then the two triangles are congruent. (ASA) | Real World Relation: Congruent Trees
20: 20 | Polygons | 1. A polygon is a plane figure that is formed by three or more sides. Each side intersects exactly two other sides at each of it's endpoints. Each endpoint is a vertex of the polygon. | 2. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. | 3. A rhombus is a parallelogram with four congruent sides. | 4. A triangle has 3 sides. | 5. A quadrilateral has 4 sides.
21: 21 | 6. A rectangle is a parallelogram with four right angles. | 7. A square is a parallelogram with four congruent sides and four right angles. | Real World Relation: White Board | 8. A pentagon has 5 sides. | 9. A hexagon has 6 sides. | 10. A heptagon has 7 sides. | 11. A octagon has 8 sides.
22: 22 | 1. Collinear points are points that lie on the same line. | Extra Credit | 2. Coplanar points are points that lie on the same plane. | 3. Coplanar lines are lines that lie on the same plane.
23: 23 | 4. A line has one dimension. It extends without end in two directions. It is represented by a line with two arrowheads. | 5. A 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.