BC: A Good Beginning Makes a Good Ending
FC: First Semester Geometry Scrapbook Third Period Sedona Tooley December 12, 2012
1: 1 | Table of Contents Page 2 & 3 - Geometry Basics Page 4 &5 - Angles and Their Measures Page 6 & 7 -Angle and Segment Bisectors Page 8 & 9 - Complementary, Supplementary, and Vertical Angles Page 10 & 11 - Parallel Lines and Angles Formed by Transversals 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
2: Geometry Basics Point- has no dimension. It is represented by a red dot. Line- has one dimension. It extends without end in two directions. It is represented by a line with two arrowheads. Plane- has two dimensions. It is represented by a shape that looks like a floor or wall. Postulates- are statements that are accepted without further justification. | 2
3: 3 | Real World Example These uncooked spaghetti pieces are like lines. They are straight and go in two different directions.
4: 4 | Angles and Their Measures angle- a figure formed by two lines extending from the same point obtuse angle- an angle between 90 and 180 degrees acute angle- an angle less than 90 degrees but more than 0 degrees straight angle- and angle of 180 degrees parallel lines- Two lines on a plane that never meet. They are always the same distance apart.
5: 5 | Two sides of the fan form an obtuse angle. This sign makes a right angle.
6: 6 | Angle and Segment Bisectors Angle- a figure formed by two lines extending from the same point Angle Bisector-a ray that divides an angle into into two equal parts Segment Bisector- a segment, ray, line, or plane that intersects a segment at its midpoint | angle | segment bisector | angle bisector
7: 7 | Real Life Example of An Angle Bisector This baseball field has an angle bisector. First, third, and home base make a right angle. The bisector starts at home base and goes through second base.
8: 8 | Complementary, Supplementary, and Vertical Angles Complementary angles- either of two angles whose sum is 90 degrees Supplementary angles- either of two angles whose sum is 180 degrees Vertical angles- either of two angles lying on opposite sides of two intersecting lines
9: 9 | Real World Example These skis crossed over each other make a vertical angle.
10: 10 | Parallel Lines and Angles Formed by Transversals Parallel lines- two lines that lie in the same plane and do not intersect Corresponding angles- two angles that occupy corresponding positions Alternate interior angles- two angles that lie between the two lines on the opposite sides of the transversal Alternate exterior angles- two angles that lie outside the two lines on the opposite sides of the transversal Same-side interior angles- two angles that lie between the two lines on the same side of the transversal
11: 11 | Real World Example This leaf has angles on it. You can see all angles formed by transversals on it.
12: 12 | Perpendicular Lines Perpendicular lines- two lines that intersect to form a right angle
13: 13 | Real World Example The wood between the window panes make perpendicular lines.
14: 14 | Triangles Triangle- a figure formed by three segments joining three noncollinear points Equilateral Triangle- has three congruent sides Isosceles Triangle- has at least two congruent sides Scalene Triangle- has no congruent sides Equiangular Triangle- has three congruent angles Right Triangle- has one right angle Acute Triangle- has three acute angles Obtuse Triangle- has one obtuse angle
15: 15 | Real World Example This pool triangle is an equilateral triangle.
16: 16 | The Pythagorean Theorem and the Distance Formula 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 Hypotenuse- the side opposite the right angle The Distance Formula- If A and B are points in a coordinate plane, then the distance between A and B is
17: 17 | Real World Example This slope shows the Pythagorean Theorem.
18: 18 | Congruent Triangles 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 are 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 Postulate- 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 triangle, then the two triangles are congruent. Hypotenuse Leg- 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
19: 19 | Real World Example This garden has en enclosed area that is like the hypotenuse leg postulate.
20: 20 | Polygons Polygon- a plane figure that is formed by three or more segments Parallelogram- a quadrilateral with both pairs of opposite sides parallel Rhombus- a parallelogram with four congruent sides Rectangle- a parallelogram with four right angles Square- a parallelogram with four congruent sides and four right angles
21: 21 | Real World Example This paint on the road is a parallelogram.