BY: ANA JULIA ROGOZINSKI (YOLO). -A ratio is a comparison between one number to another number. In ratios you generally separate the numbers using a colon.

Slides:



Advertisements
Similar presentations
Ratios, Proportions, AND Similar Figures
Advertisements

Review Chapter 4.
Trigonometry Exit Definitions sine cosine & tangent adjacent side opposite side angle hypotenuse Terminology.
Cristian Brenner.  A ratio is when you compare two numbers by division. A ratio may contain more then two number that may compare the sides of a triangle.
Chapter 7 and 8 By: Ou Suk Kwon. Comparing 2 numbers that are written: A to B A / B A:B.
Warm Up for Section 1.2 Simplify: (1). (2). (3). There are 10 boys and 12 girls in a Math 2 class. Write the ratio of the number of girls to the number.
Using Proportions to Solve Geometry Problems Section 6.3.
Geometry One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Today: 9.5 Instruction Practice.
MA.912.T.2.1 CHAPTER 9: RIGHT TRIANGLES AND TRIGONOMETRY.
Christa Walters 9-5 May When using a ratio you express two numbers that are compared by division. Can be written as: a to b a:b a b.
abababb RATIO – a ratio compares two numbers by dividing. The ratio of two numbers can be written in various ways such as a to b, a:b, or a/b, where b.
Geometry Journal Chapter 7 & 8 By: Jaime Rich. A comparison of two numbers by division. An equation stating that two ratios are equal. You solve proportions.
Section 11 – 1 Simplifying Radicals Multiplication Property of Square Roots: For every number a > 0 and b > 0, You can multiply numbers that are both under.
Chapter 8 By Jonathan Huddleston. 8-1 Vocab.  Geometric Mean- The positive square root of the product of two positive numbers.
Journal Chapters 7 & 8 Salvador Amaya 9-5. Ratio Comparison of 2 numbers written a:b, a/b, or a to b.
Visual Glossary By: Anya Khosla Unit 6. Introduction Most people in this world know how to read. Everywhere you go, people are always reading. From s.
Unit 4: Right Triangles Triangle Inequality
Solve the following proportions. a = 9 b = 7 c = 6 d = 6.
STUDY GUIDE FOR TRIG. FOR TUESDAY’S TEST IN MRS. GOODHUE’S CLASS! BY: MRS. CAMUTO.
Unit 7 Similarity. Part 1 Ratio / Proportion A ratio is a comparison of two quantities by division. – You can write a ratio of two numbers a and b, where.
 Ratio: is the comparison of two numbers by division  Ratio of two numbers can be shown like this; a to b, a:b, or a/b  Proportion: equation that says.
5.3 Apply the SINE and COSINE ratios We will look at the TANGENT ratio tomorrow!
 Ratio: Is a comparison of two numbers by division.  EXAMPLES 1. The ratios 1 to 2 can be represented as 1:2 and ½ 2. Ratio of the rectangle may be.
Solve the following proportions. a = 9 b = 7 c = 6 d = ±6.
J OURNAL C HAPTER 7- 8 Marcela Janssen. C HAPTER 7: S IMILARITY.
1 10/16/12 Triangles Unit Similar Polygons. 2 Definition:Two polygons are similar if: 1. Corresponding angles are congruent. 2. Corresponding sides are.
Ms. Drake 7th grade Math Fractions Lesson 44 Similar Figures and Proportions.
Daniela Morales Leonhardt 9-5. _____(0-10 pts) Describe a ratio. Describe a proportion. How are they related? Describe how to solve a proportion. Describe.
____(0-10 pts) Describe a ratio. Describe a proportion. How are they related? Describe how to solve a proportion. Describe how to check if a proportion.
Special Right Triangles Definition and use. The Triangle Definition  There are many right angle triangles. Today we are most interested in right.
Ratio and Proportion Students will be able to write and simplify ratios and to use proportions to solve problems.
Unit 1 Transformations Day 5.  Similar Polygons - Two figures that have the same shape but not necessarily the same size ◦ Symbol: ~ ◦ Similar Polygons.
Ratio and Proportion Day 8. Day 8 Math Review Math Review Quiz Day.
 Two polygons are similar polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional.
A ratio is a quotient of two numbers. The ratio of two numbers, a & b can be written as a to b, a:b, or a/b, (where b = 0). Examples: to 21:21/2.
By: Katerina Palacios similar polygons: When 2 polygons are similar that means that they have the same looking shape but they do not have the.
Chapter 7 & 8 Kirsten Erichsen Journal Geometry. RATIOS AND PROPORTIONS.
 The study of triangles  Relationship between sides and angles of a right triangle › What is a right triangle? A triangle with a 90 ⁰ angle 90°
Similarity. Do Now What is the volume of the prism below: 3 in 2 in 7 in.
The relation between a ratio and a proportion is: the proportion shows that two ratios are equal. If 84 is divided into three parts in the ratio 3:5:6,
What is a Ratio? A Ration is a comparison of two numbers. Usually it separates the two numbers is colon (:). It can be writen as a to b, A:B, A/B There.
Notes Chapter 8.3 Trigonometry  A trigonometric ratio is a ratio of the side lengths of a right triangle.  The trigonometric ratios are:  Sine: opposite.
Solving Right Triangles using Trigonometry. Labeling a Right Triangle  In trigonometry, we give each side a name according to its position in relation.
Describe a ratio. Describe a proportion. How are they related? Describe how to solve a proportion. Describe how to check if a proportion is equal. Give.
Marcos Vielman 9-5.  A ratio compares two numbers by division.  A proportion is an equation starting that two ratios are equal.  They are related because.
Chapter 8.1 Notes Ratio – if a and b are 2 quantities that are measured in the same units, then the ratio of a to b is a/b. (i.e. a ratio is a fraction)
7.1 Proportions Solving proportions
Trigonometric Functions
Angles of Elevation and Depression
Y. Davis Geometry Notes Chapter 7.
Similar Polygons & Scale Factor
Geometry Final Vocabulary
Geometry Final Vocabulary
Chapter 2 Similarity and Dilations
CHAPTER 10 Geometry.
Using Proportions with Similar Figures
Similar Polygons & Scale Factor
Similar Polygons & Scale Factor
Lesson 6.1 How do you find ratios and unit rates?
SIMILAR POLYGONS Two figures are similar if
Similar Polygons & Scale Factor
Warm Up 1. If ∆QRS  ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion Q  Z; R 
Similar Polygons & Scale Factor
Y. Davis Geometry Notes Chapter 8.
Introduction to Trigonometry
Similar Polygons & Scale Factor
Similar Polygons & Scale Factor
Rates, Ratios and Proportions
Unit 4: Similarity Honors Geometry.
Geometry Final Vocabulary
Presentation transcript:

BY: ANA JULIA ROGOZINSKI (YOLO)

-A ratio is a comparison between one number to another number. In ratios you generally separate the numbers using a colon ( : ) between them or using a fraction. Alexandra has in her backpack 7 books, 13 crayons, 2 pencils, and 8 markers. 1.If you want to write the ratio of books to crayons, you would write it 7:13 2. If you want to write the ratio of pencils to markers, you would write it 2:8 3. If you want to write the ratio of pencils to crayons, you would write 2:13 4. The ratio of the side lengths of a quadrilateral is 2:4:5:7 and its perimeter is 36m. What is the length of the longest side? 2x +4x+5x+7x=36 18x=36 x=2 7(2) = 14

-A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. In a proportion a/b = c/d, a and d are the extremes and b and c are the means. 1.3:4 = 6:8 or 3/4 = 6/8 2.8:10 = 4:5 or 8/10 = 4/ :15 = 5:3 or 25/15 = 5/3 4. 2:3 = 16:24 or 2/3 = 16/24

- A ratio and a proportion are related in the form that a ratio relates two quantities together using a fraction, and a proportion establishes a relationship between two quantities. Also they both show an equation with a ratio. - To solve a proportion you use cross products property. ( The product of the extremes is equal to the product of the means). If one term of a proportion is not known, cross multiplication can be used to find the value of that term. For example a/b = c/d, then ad=bc. 1. x/2= 40/ /y = 21/27 3. x²/18 = x/ 6 16x = = 21y √6x² = √18x x=5 9=y x=3 or x=0

-To check if a proportion is equal you simplify both fractions until they are both equal, then if they are you have it correct meaning that they are equal if not you may have done something wrong. 1. 6/8 and 3/4, you reduce 6/8 to 3/4 2.15/25 and 5/3, you reduce 15/25 to 5/3 3. 8/10 and 4/5, you reduce 8/10 to 4/5 so both are equal.

- Similar figures don’t necessarily need to have the same size but they do need to have the same shape. Two polygons with corresponding angles congruent and their corresponding side lengths are proportional are SIMILAR POLYGONS. YES NO

- A Scale Factor describes how much the figure is enlarged or reduced. It’s used on each dimension in order to change one figure into a similar figure. As well it is a form of describing how the sides of a polygon re different DILATION: transformation that changes the size of the figure but not its shape.

INDIRECT MEASUREMENT: any method that uses formulas, similar figures or proportions to measure an object. -To make an indirect measurement by using similar triangles you use the given measurements and information in order to find your answer. This is an important skill because there are many ways to use in real life, for example when you want to find the measurement of tall objects for example buildings, trees, etc.

-To find the scale factor for the perimeter and areas of similar figures you need to see the corresponding sides which are proportional and the corresponding angles are equal. The scale factor describes the difference between the side it also describes how much a figure is enlarged or reduced. PERIMETER: when you have the perimeter of both triangles then form fractions putting the smaller shape over the bigger shape and simplify. The ratio is the same as the ratio of their sides. AREA: Follow the same steps as in finding the perimeter but after you have made the fractions then simplify them all it can, and then you square them.

Perimeter: 2/3 Area:4²/9² Perimeter: 14(4)=56 24(24)=96 56/96=7/ Area: 8/16=2²/4² Perimeter: 36/72 = 1/2 Area: if sides where 8 and 24 8/24= 1²/3²

-A trigonometric ratio is the ratio a two sides of a triangle. - The three Trigonometric function are Sine, Cosine, and Tangent. SinA is the ratio of the length of the opposite side / hypotenuse CosA is the ratio of the adjacent / hypotenuse (between 0 and 1) TanA is ratio of the opposite / adjacent IN pposite ypotenus e OS djacent ypotenus e AN pposite djacent hypotenuse adjacent opposite

-They can be used to solve a right triangle because it helps you find the missing sides and angles of the triangle. -To solve a triangle means to find every angle and side of it. 1. B A SinA: 6/10= 3/5 CosA: 8/10 = 4/5 Tan= 6/8 = 3/4 Using the converse you know that A=37 and B= SinA: 5/13 CosA:12/13 TanA:5/12 3. SinB: 12/13 CosB:5/13 TanB:12/5

-An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line. -An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line. - They are different in the fact that the angle of elevation is above the line and the angle of depression below the line.They are similar in the fact that both are angles formed with a horizontal line. Angle of elevation Angle of depression

1. How is the angle that the arrow is pointing called? ANGLE OF ELEVATION 2. What would “x” be representing? The angle of elevation Tan25=5/x 5/tan25=x x=4.3