FC: Geometry Scrapbook By: Brandon Neely 3rd Period December 12, 2012
1: Table Of Contents GEOMETRY BASICS- 2-3 ANGLES AND THEIR MEASURES- 4-5 ANGLE AND SEGMENT BISECTORS- 6-7 COMPLEMENTARY, SUPPLEMENTARY, AND VERTICAL ANGLES- 8-9 PARALLEL LINES AND ANGLES FORMED BY TRANSVERSALS- 10-11 PERPENDICULAR LINES- 12-13 TRIANGLES (CLASSIFYING, ANGLE MEASUREMENTS, ETC.)- 14-15 PYTHAGOREAN THEOREM AND DISTANCE FORMULA- 16-17 CONGRUENT TRIANGLES (INCLUDING THE 5 WAYS TO PROVE GRUENCY)- 18-19 POLYGONS (PARELLELOGRAMS, RHOMBUSES, RECTANGLES, AND SQUARES)- 20-21
2: Point- Has no dimension. It is represented by a small dot. Line- Has one dimension. It extends without end in two directions. Represented by a line with two arrowheads. Plane- Has two dimensions. It is represented by a shape that looks like a wall or a floor.
3: PLANE | LINE | POINT
4: Obtuse Angle- An angle that is above 90 degrees but below 180 degrees. Acute Angle- An angle that is below 90 degrees but above 0. Straight Angle- An angle that is 180 degrees, straight.
5: STRAIGHT LINE | ACUTE ANGLE | OBTUSE ANGLE
6: Bisect- Is to divide the segment into two congruent segments. Segment Bisector- Is a segment, ray, line, or plane that intersects a segment at its midpoint. Angle Bisector- Is a ray that divides an angle into two angles that are congruent.
7: SEGMENT BISECTOR & ANGLE BISECTOR | BISECT
8: Complementary Angles- Two angles are Complementary if the sum of their measures is 90 degrees. Supplementary Angles- Two angles are Supplementary if the sum of their measures is 180 degrees. Vertical Angles- Two angles are Vertical Angles if they are not adjacent and their sides are formed by two intersecting lines.
9: SUPPLEMENTRY ANGLE | COMPLEMENTRY ANGLES | VERTICAL ANGLES
10: Parallel Lines- Two lines are Parallel if they line in the same plane or don't intersect. Transversal- A line that intersects two or more coplanar lines at different points. Skew Lines- Two lines are Skew if they do not lie in the same plane.
11: PARALLEL LINES | SKEW LINES | TRANSVERSAL
12: Perpendicular Lines- Two lines are Perpendicular lines if they intersect to form a right angle Line Perpendicular to a Plane- is a line that intersects a plane in a point and that is perpendicular to every line in the plane that intersect it
13: PERPENDICULAR LINES
14: Equilateral Triangle- 3 congruent sides. Isosceles Triangle- At least 2 congruent sides. Scalene Triangle- No congruent sides. Equiangular Triangle- 3 congruent angles.
15: Obtuse Triangle- 1 obtuse angle. Right Triangle- 1 right angle. Acute Triangle- 3 acute angles.
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. Distance Formula- Gives the distance between two points in a coordinate plane.
17: DISTANCE FORMULA
18: Corresponding Parts of Congruent Figures- The corresponding sides and angles in congruent figures. SSS- Three sides of one triangle have the same lengths as the three sides of another triangle, then the two triangles are congruent. SAS- Any two sides of a triangle are equal in length to two sides of another triangle and the angles between each pair of sides have the same measure, then the two triangles are congruent.
19: ASA- If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the two triangles are congruent. AAS- If two angles and the non-included side one triangle are congruent to two angles and the non-included angle of another triangle, then these two triangles are congruent. HL- Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
20: Polygon- A plane figure with at least three straight sides and angles. Parallelogram- A four sided plane rectilinear figure with opposite sides parallel. Rhombus- A parallelogram with opposite equal acute and obtuse angles and four equal sides. Rectangle- A plane figure with four straight sides and four right angles, esp. one with unequal adjacent sides, in contrast to a square. Square- A plane figure with four equal straight sides and four right angles.
21: RHOMBUS & PARALLELOGRAM | RECTANGLE | POLYGON | SQUARE