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# geomentry scrapbook

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BC: THE END

FC: Geometry Flashback Scrapbook! | BY:JESSICA FREDERICK THIRD PERIOD DECEMBER 12, 2012

1: Title Page 1: Table of Contents Page 2-3: Geometry Basics from Sections 1.1-1.5 Page 4-5: Angles and their Measures Page 6-7: Angle and Segment Bisectors Page 8-9: Complementary, Supplementary, and Vertical Angles Page10-11: Parallel Lines and Angles formed by a Transversal Page 12-13: Perpendicular Lines Page 14-15: Triangles Page 16-17: Pythagorean Theorem and Distance Formula Page 18-19: Congruent Triangles Page 20-21: Polygons Page 22-23: Bonus

2: POINT Has no dimension. A point is represented by a dot. | LINE A line only has one dimension; a line extends in two directions without an end.

3: PLANE A plane has two dimensions; a plane is represented by a shape that extends without an end.

4: ANGLE An angle consists of two rays that have the same endpoint. | Acute Angle o degrees to 90 degrees | Straight Angle 180 degrees | Right Angle 90 degrees | Obtuse Angle 90 degrees to 180 degrees

5: REAL WORLD ENCOUNTERS WITH ANGLES | ACUTE | OBTUSE | RIGHT

6: SEGMENT BISECTOR A segment bisector is a segment, ray, line, or plane that intersects a segment at its point.

7: Angle Bisector An angle bisector is a ray that divides an angle into tow angles that are congruent.

8: COMPLEMENTARY ANGLES Complementary angles is if the sum equals ninety 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: COMPLEMENTARY | VERTICAL | SUPPLEMENTARY | EXAMPLES

10: PARALLEL LINES Parallel lines are lines that lie in the same plane and do not intersect. | TRANSVERSAL A transversal is a line that intersects two or more coplanar lines at different points

11: Corresponding Angles- Occupy opposite positions | Alternate Interior Angles- Lie between the two lines | Alternate Exterior Angles- Lie outside the two lines | Same Side Interior Angles- Lie between the two lines on the same side of the transversal.

12: PERPENDICULAR LINES Perpendicular lines are two lines that intersect to form a right triangle.

13: EXAMPLES

14: TRIANGLES A triangle is a figure formed by three segments joining three non-collinear points. Triangles are classified by there angles. | Identifying Angles by Sides | Equilateral- 3 congruent sides | Isosceles- 2 congruent sides | Scalene- no congruent sides

15: Identifying Triangles by Angles | Equiangular- 3 congruent angles | Right- one right angle | Acute- 3 acute angles | Obtuse- 1 obtuse angle

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 The distance formula gives the distance between two points in a coordinate plane.

18: CONGRUENT TRIANGLES | Triangles are congruent if all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent. | HL | SSS | SAS | AAS | ASA

19: FIVE WAYS TO PROVE CONGRUENCY | Side-Side-Side Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. | Side-Angle- Side Congruence Postulate If two sides and the included angle of one triangle ate congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. | Angle-SIde-Angle Congruence Postulate 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. | Angle-Angle-Side Congruence Theorem If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then the two triangles are congruent. | Hypotenuse-Leg Congruence Theorem 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

20: POLYGONS A polygon is a plane figure that is formed by three or more segments. | Triangle | Quadrilateral | Hexagon | Heptagon | Octagon | Pentagon | Three Sides | Four SIdes | Six Sides | Seven SIdes | Five Sides | Eight sides.

21: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. | Rhombus- parallelogram with four congruent sides. | Rectangle- parallelogram with four right angles | Square- parallelogram with four congruent sides and four right angles | PARALLELOGRAM

22: LEGS The nonparallel sides are the legs. | BASES The parallel sides are called bases | TRAPEZOID A trapezoid is a quadrilateral with exactly one pair of parallel sides. | BASE ANGLES A trapezoid has two base angles. | ISOSCELES TRIANGLE If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

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• By: Jessica F.
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