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## CIRCLES

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**CIRCLES**BASIC TERMS AND FORMULAS Natalee Lloyd**Terms**Center Radius Chord Diameter Circumference Formulas Circumference formula Area formula Basic Terms and Formulas**Center: The point which allpoints of the circle are**equidistant to.**Radius: The distance from the center to a point on the**circle**Diameter: A chord that passes through the center of the**circle.**Circumference Example**C = 2r C = 2(5cm) C = 10 cm 5 cm**Area Example**A = r2Since d = 14 cm then r = 7cm A = (7)2 A = 49 cm 14 cm**Angles in Geometry**Fernando Gonzalez - North Shore High School**Intersecting Lines**• Two lines that share one common point. Intersecting lines can form different types of angles.**Complementary Angles**• Two angles that equal 90º**Supplementary Angles**• Two angles that equal 180º**Corresponding Angles**• Angles that are vertically identical they share a common vertex and have a line running through them**Geometry**Basic Shapes and examples in everyday life Richard Briggs NSHS**GEOMETRY**Exterior Angle Sum Theorem**What is the Exterior Angle Sum Theorem?**• The exterior angle is equal to the sum of the interior angles on the opposite of the triangle. 40 70 70 110 110 = 70 +40**Exterior Angle Sum Theorem**• There are 3 exterior angles in a triangle. The exterior angle sum theorem applies to all exterior angles. 128 52 64 64 116 116 128 = 64 + 64 and 116 = 52 + 64**Linking to other angle concepts**• As you can see in the diagram, the sum of the angles in a triangle is still 180 and the sum of the exterior angles is 360. 160 20 100 80 80 100 80 + 80 + 20 = 180 and 100 + 100 + 160 = 360**Geometry**Basic Shapes and examples in everyday life Barbara Stephens NSHS**GEOMETRY**Interior Angle Sum Theorem**What is the Interior Angle Sum Theorem?**• The interior angle is equal to the sum of the interior angles of the triangle. 40 70 70 110 110 = 70 +40**Interior Angle Sum Theorem**• There are 3 interior angles in a triangle. The interior angle sum theorem applies to all interior angles. 128 52 64 64 116 116 128 = 64 + 64 and 116 = 52 + 64**Linking to other angle concepts**• As you can see in the diagram, the sum of the angles in a triangle is still 180. 160 20 100 80 80 100 80 + 80 + 20 = 180**Geometry**Parallel Lines with a Transversal Interior and exterior Angles Vertical Angles By Sonya Ortiz NSHS**Transversal**• Definition: • A transversal is a line that intersects a set of parallel lines. • Line A is the transversal A**Interior and Exterior Angles**• Interior angels are angles 3,4,5&6. • Interior angles are in the inside of the parallel lines • Exterior angles are angles 1,2,7&8 • Exterior angles are on the outside of the parallel lines 1 2 3 4 5 6 7 8**Vertical Angles**• Vertical angles are angles that are opposite of each other along the transversal line. • Angles 1&4 • Angles 2&3 • Angles 5&8 • Angles 6&7 • These are vertical angles 1 2 3 4 5 6 7 8**Summary**• Transversal line intersect parallel lines. • Different types of angles are formed from the transversal line such as: interior and exterior angles and vertical angles.**Geometry**Parallelograms M. Bunquin NSHS**Parallelograms**• A parallelogram is a a special quadrilateral whose opposite sides are congruent and parallel. A B D C • Quadrilateral ABCD is a parallelogram if and only if • AB and DC are both congruent and parallel • AD and BC are both congruent and parallel**Kinds of Parallelograms**• Rectangle • Square • Rhombus**Rectangles**• Properties of Rectangles • 1. All angles measure 90 degrees. • 2. Opposite sides are parallel and congruent. • 3. Diagonals are congruent and they bisect each other. • 4. A pair of consecutive angles are supplementary. • 5. Opposite angles are congruent.**Squares**• Properties of Square • 1. All sides are congruent. • 2. All angles are right angles. • 3. Opposite sides are parallel. • 4. Diagonals bisect each other and they are congruent. • 5. The intersection of the diagonals form 4 right angles. • 6. Diagonals form similar right triangles.**Rhombus**• Properties of Rhombus • 1. All sides are congruent. • 2. Opposite sides parallel and opposite angles are congruent. • 3. Diagonals bisect each other. • 4. The intersection of the diagonals form 4 right angles. • 5. A pair of consecutive angles are supplementary.**Geometry**Pythagorean Theorem Cleveland Broome NSHS**Pythagorean Theorem**• The Pythagorean theorem • This theorem reflects the sum of the squares of the sides of a right triangle that will equal the square of the hypotenuse. C2 =A2 +B2**A right triangle has sides a, b and c.**c b a If a =4 and b=5 then what is c?**Calculations:**A2 + B2 = C2 16 + 25 = 41**To further solve for the length of C**Take the square root of C 41 = 6.4 This finds the length of the Hypotenuse of the right triangle.**The theorem will help calculate distance when traveling**between two destinations.**GEOMETRY**Angle Sum Theorem By: Marlon Trent NSHS**Triangles**• Find the sum of the angles of a three sided figure.**Quadrilaterals**• Find the sum of the angles of a four sided figure.**Pentagons**• Find the sum of the angles of a five sided figure.**Hexagon**• Find the sum of the angles of a six sided figure.**Heptagon**• Find the sum of the angles of a seven sided figure.**Octagon**• Find the sum of the angles of an eight sided figure.