BASIC TERMS AND FORMULAS Natalee Lloyd CIRCLES BASIC TERMS AND FORMULAS Natalee Lloyd

Basic Terms and Formulas Center Radius Chord Diameter Circumference Formulas Circumference formula Area formula

Center: The point which all points of the circle are equidistant to.

Radius: The distance from the center to a point on the circle

Chord: A segment connecting two points on the circle.

Diameter: A chord that passes through the center of the circle.

Circumference: The distance around a circle.

Circumference Formula: C = 2r or C = d Area Formula: A = r2

Circumference Example C = 2r C = 2(5cm) C = 10 cm 5 cm

Area Example A = r2 Since d = 14 cm then r = 7cm A = (7)2 A = 49 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

Basic Shapes and examples in everyday life Geometry Basic Shapes and examples in everyday life Richard Briggs NSHS

Exterior Angle Sum Theorem 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

Basic Shapes and examples in everyday life Geometry Basic Shapes and examples in everyday life Barbara Stephens NSHS

Interior Angle Sum Theorem 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. 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.

Angle Sum Theorem By: Marlon Trent NSHS 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.

Complete The Chart Triangle Quadrilateral Pentagon Hexagon Heptagon Name of figure Number of sides Sum of angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Decagon n-agon

What is the angle sum formula? Angle Sum=(n-2)180 Or Angle Sum=180n-360

A presentation by Mary McHaney

THE SQUARE IS A RECTANGLE OR THE RECTANGLE IS A SQUARE A SQUARE IS RECTANGLE QUADRILATERAL DILEMMA THE SQUARE IS A RECTANGLE OR THE RECTANGLE IS A SQUARE

SQUARE Characteristics: Four equal sides Four Right Angles

RECTANGLE Characteristics Opposite sides are equal Four Right Angles

Square and Rectangle share Four right angles Opposite sides are equal

SQUARE AND RECTANGLE DO NOT SHARE: All sides are equal

SO A SQUARE IS RECTANGLE A RECTANGLE IS NOT A SQUARE

Charles Upchurch

Triangles Are Classified Into 2 Main Categories. Types of Triangles Triangles Are Classified Into 2 Main Categories.

Triangles Classified by Sides

Triangles Classified by Their Sides Scalene Triangles These triangles have all 3 sides of different lengths.

Isosceles Triangles These triangles have at least 2 sides of the same length. The third side is not necessarily the same length as the other 2 sides.

Equilateral Triangles These triangles have all 3 sides of the same length.

Triangles Classified by their Angles

Acute Triangles These Triangles Have All Three Angles That Each Measure Less Than 90 Degrees.

Right Triangles These triangles have exactly one angle that measures 90 degrees. The other 2 angles will each be acute.

Obtuse Triangles These triangles have exactly one obtuse angle, meaning an angle greater than 90 degrees, but less than 180 degrees. The other 2 angles will each be acute.

A polygon that has four sides Quadrilaterals A polygon that has four sides Paulette Granger

Quadrilateral Objectives Upon completion of this lesson, students will: have been introduced to quadrilaterals and their properties. have learned the terminology used with quadrilaterals. have practiced creating particular quadrilaterals based on specific characteristics of the quadrilaterals.

Parallelogram                                             A quadrilateral that contains two pairs of parallel sides

Rectangle A parallelogram with four right angles

Square A parallelogram with four congruent sides and four right angles

Group Activity Each group design a different quadrilateral and prove that its creation fits the desired characteristics of the specified quadrilateral. The groups could then show the class what they created and how they showed that the desired characteristics were present.

Classifying Angles Dorothy J. Buchanan--NSHS Geometry Classifying Angles Dorothy J. Buchanan--NSHS

Right angle 90° Straight Angle 180°

Examples Acute angle 35° Obtuse angle 135°

If you look around you, you’ll see angles are everywhere If you look around you, you’ll see angles are everywhere. Angles are measured in degrees. A degree is a fraction of a circle—there are 360 degrees in a circle, represented like this: 360°. You can think of a right angle as one-fourth of a circle, which is 360° divided by 4, or 90°. An obtuse angle measures greater than 90° but less than 180°.

Complementary & Supplementary Angles Olga Cazares North Shore High School

Complementary Angles Complementary angles are two adjacent angles whose sum is 90° 60 ° 30 ° 60 ° + 30 ° = 90°

Supplementary Angles Supplementary angles are two adjacent angles whose sum is 180° 120° 60° 120° + 60° = 180°

Application First look at the picture. The angles are complementary angles. Set up the equation: 12 + x = 180 Solve for x: x = 168° 12° x

Right Angles by Silvester Morris

RIGHT ANGLES RIGHT ANGLES ARE 90 DEGREE ANGLES.

STREET CORNERS HAVE RIGHT ANGLES SILVESTER MORRIS NSHS

Parallel and Perpendicular Lines by Melissa Arneaud

Recall: Equation of a straight line: Y=mX+C Slope of Line = m Y-Intercept = C

Parallel Lines Symbol: “||” Two lines are parallel if they never meet or touch. Look at the lines below, do they meet? Line AB is parallel to Line PQ or AB || PQ

Slopes of Parallel Lines If two lines are parallel then they have the same slope. Example: Line 1: y = 2x + 1 Line 2: y = 2x + 6 THINK: What is the slope of line 1? What is the slope of line 2? Are these two lines parallel?

Perpendicular Lines Two lines are perpendicular if they intersect each other at 90°. Look at the two lines below: A D C B Is AB perpendicular to CD? If the answer is yes, why?

Slopes of Perpendicular Lines The slopes of perpendicular lines are negative reciprocals of each other. Example: Line 3: y = 2x + 5 Line 4: y = -1/2 x + 8 THINK: What is the slope of line 3? What is the slope of line 4? Are these two lines perpendicular. If so, why? Show your working.

What do you need to know Parallel Lines Perpendicular Lines Do not intersect. If two lines are parallel then their slopes are the same. Perpendicular Lines Intersect at 90°(right angles). If two lines are perpendicular then their slopes are negative reciprocals of each other.

Questions Write an equation of a straight line that is parallel to the line y = -1/3 x + 7 State the reason why your line is parallel to that of the line given above. Write an equation of a straight line that is perpendicular to the line y = 4/5 x + 3. State the reason why the line you chose is perpendicular to the line given above.

Basic Shapes by Wanda Lusk

Two Dimensional Length Width Basic Shapes Two Dimensional Length Width Three Dimensional Length Width Depth (height)

Basic Shapes Two Dimensions Circle Triangle Parallelogram Square Rectangle

Basic Shapes Two Dimensions Circle

Basic Shapes Two Dimensions Triangle

Basic Shapes Two Dimensions Square

Basic Shapes Two Dimensions Square Rectangle

Basic Shapes Three Dimensions Sphere Cone Cube Pyramid Rectangular Prism

Basic Shapes Three Dimensions Sphere Cone Cube Pyramid Rectangular Prism