similar right triangles common core geometry homework answers

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Common Core: High School - Geometry : Similarity, Right Triangles, & Trigonometry

Study concepts, example questions & explanations for common core: high school - geometry, all common core: high school - geometry resources, example questions, example question #1 : dilations given center and scale factor: ccss.math.content.hsg srt.a.1.

If the red figure is an object and the blue figure is an object after dilation, what is the scale factor?

The best way to solve for the scale factor is to find the same vertex from each object, and divide their components.

Let's divide the x-coordinates together.

Since we are going from the smaller object to the larger object, we know that our scale factor is going to be greater than one.

So our final answer is going to be.

Example Question #2 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

Example Question #3 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

Example Question #4 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

Example Question #5 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

If the blue figure is an object and the red is an object after dilation, what is the scale factor?

Since we are going from the larger object to the smaller object, we know that our scale factor is going to be less than one.

Example Question #1 : Similarity, Right Triangles, & Trigonometry

Example Question #7 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

Example Question #8 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

Example Question #9 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

Example Question #10 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

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Mathematics Glossary

Mathematics » high school: geometry » similarity, right triangles, & trigonometry, standards in this domain:, understand similarity in terms of similarity transformations.

• A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
• The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
• G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
• G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Prove theorems involving similarity

• G-SRT.4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
• G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Define trigonometric ratios and solve problems involving right triangles

• G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
• G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles.
• G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★

Apply trigonometry to general triangles

• G-SRT.9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
• G-SRT.10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
• G-SRT.11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
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Calcworkshop

Similar Right Triangles Fully Explained w/ 9 Examples!

// Last Updated: January 21, 2020 - Watch Video //

In today’s geometry lesson, you’re going to learn all about similar right triangles.

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

More specifically, you’re going to see how to use the geometric mean to create proportions, which in turn help us solve for missing side lengths.

Let’s get started!

How are right triangles and the geometric mean related?

The two legs meet at a 90° angle, and the hypotenuse is the side opposite the right angle and is the longest side.

Right Triangle Diagram

The geometric mean of two positive numbers a and b is:

Geometric Mean of Two Numbers

And the geometric mean helps us find the altitude of a right triangle! In fact, the geometric mean, or mean proportionals, appears in two critical theorems on right triangles.

Geometric Mean Theorems

In a right triangle, if the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.

Altitude Rule

Additionally, the length of each leg is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg, as ck-12 accurately states.

But what do these theorems really mean?

They help us to create proportions for finding missing side lengths!

Let’s look at an example!

How To Solve Similar Right Triangles

In the figure below, we are being asked to find the altitude, using the geometric mean and the given lengths of two segments:

Using Similar Right Triangles

In the video below, you’ll learn how to deal with harder problems, including how to solve for the three different types of problems:

• Missing Altitude
• Missing Leg
• Missing Segment of a Leg

Video – Lesson & Examples

• Introduction
• 00:00:29 – 2 Important Theorems
• Exclusive Content for Member’s Only
• 00:13:21 – What is the length of the altitude drawn to the hypotenuse? (Examples #1-6)
• 00:25:47 – The altitude to hypotenuse is drawn in a right triangle, find the missing length (Examples #7-9)
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Common Core Geometry Math (Worksheets, Homework, Lesson Plans)

Related Topics: Common Core Math Resources, Lesson Plans & Worksheets for all grades Common Core Math Video Lessons, Math Worksheets and Games for Geometry Common Core Math Video Lessons, Math Worksheets and Games for all grades

Looking for video lessons that will help you in your Common Core Geometry math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Geometry students?

The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. Eureka/EngageNY Math Geometry Worksheets.

These Lesson Plans and Worksheets are divided into five modules.

Geometry Homework, Lesson Plans and Worksheets

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Common Core Geometry - Unit #8 Right Triangle Trigonometry

Description

This 6-lesson unit contains lessons that develop and apply right triangle trigonometry. Initial lessons emphasize the connection of trigonometry to similar right triangles. Trigonometric ratios are used in later lessons to find missing sides and missing angles in right triangles. Two lessons on applying trigonometric ratios are included.

To access the lesson videos on YouTube, use your smartphone or tablet to scan the QR code at the top of each lesson.

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Geometry: Common Core (15th Edition)

By charles, randall i., chapter 7 - similarity - 7-3 providing triangles similar - practice and problem-solving exercises - page 455: 11, work step by step, update this answer.

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