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FC: Geometric Mixbook | John Austin Peay 3rd period 12/12/11

1: Title Page # Sections 1.1-1.5......................................2-3 Angles and Their Measures.........................4-5 Angle and Segment Bisectors......................6-7 Types of Angles......................................8-9 Parallel Lines......................................10-11 Perpendicular Lines..............................12-13 Triangles and Angle Measures..................14-15 Pythagorean Theorem...........................16-17 Ways to Prove Triangles Are Congruent......18-19 Polygons...........................................20-21

2: Angle: an angle consists of two rays that have the same endpoint, the rays are the sides of the angle, the endpoint is the vertex of the angle. | Coordinate: the real number that corresponds to a point is the coordinate of the point. | A Postulate: is a statement that is accepted without further justification.

3: The border of the sign and the slope inside both make angles. | Point O, is the intersection of lines CD and AB.

4: An acute angle is an angle that has a measure between 0 and 90 degrees. | A right angle has a measure of 90 degrees. | An obtuse angle has measure between 90 and 180 degrees.

5: Look closely and you can see that the tips of pencils are acute angles. Which are all between 0 and 90 degrees.

6: A segment bisector is a segment, ray, line or plane that intersects a segment at its midpoint. | An angle bisector is a ray that divides an angle into two congruent angles.

7: An intersection can be a segment bisector. | Segment AO and OB are congruent.

8: Two angles are complementary angles if the sum of their measures is 90 degrees. Each angle is the complement of the other. | Two angles are supplementary angles if the sum of their measures is 180 degrees. Each angle is the supplement of the other. | Two angles are vertical angles if they are not adjacent and their sides are not formed by two intersecting lines.

9: The line in the middle creates four ninety degree angles, or 2 supplementary angles.

10: Parallel lines are lines that lie in the same plane and do not intersect. | Two angles are same side interior angles if they lie between the two lines on the same side of the transversal | Two angles are alternate exterior angles if the lie outside the two lines on the opposite sides of the transversal

11: Two angles are corresponding angles if they occupy corresponding positions | Two angles are alternate interior angles if they lie between two lines on the opposite sides of the transversal

12: Perpendicular lines intersect to form a right angle. | Angles CBA and DBA are right angles.

14: A triangle is a figure formed by three segments joining three non-collinear points. An equilateral triangle has three congruent sides. An isosceles triangle has at least two congruent sides. A scalene triangle has no congruent sides. An equiangular triangle has three congruent angles. An acute triangle has 3 acute angles. A right triangle has on right angle. An obtuse triangle has one obtuse angle.

15: This triangle is equilateral and equiangular. | This triangle is obtuse and scalene. | The triangle on the left is right and isosceles.

16: Pythagorean theorem | a2 + b2 = c2 | Distance Formula | Example of distance formula

17: Below are two examples of Pythagorean theorem problems.

18: Congruent When all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent in two figures, the figures are congruent. | SSS Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. | ASA Congruence Postulate If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of a second triangle, then the two triangles are congruent.

19: AAS Congruence Postulate If 2 angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. | SAS Congruence Postulate If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of a second triangle, then the two triangles are congruent. | Hypotenuse Leg Congruence Postulate If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the 2 triangles are congruent.

20: If a quadrilateral is a parallelogram, then both pairs of opposite sides are parallel. | A rhombus is a parallelogram with four congruent sides. | A RECTANGLE is a parallelogram with four right angles.

21: A SQUARE is a parallelogram with four congruent sides and four congruent angles.

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