similarity common core geometry homework answers unit 7 lesson 4

Geometry: Common Core (15th Edition)

By charles, randall i., chapter 7 - similarity - 7-4 similarity in right triangles - practice and problem-solving exercises - page 465: 20, work step by step, update this answer.

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Geometry 7-4 Complete Lesson: Similarity in Right Triangles

• The hypotenuse
• The segments of the hypotenuse
• The segment of the hypotenuse adjacent to leg ST

• perpendicular
• The altitude of a triangle is a segment from a vertex to the opposite side that is __?__ to the opposite side.
• In an isosceles triangle, the altitude to the base divides the triangle into two __?__ triangles.

Common Core Geometry - Unit #7 Dilations and Similarity

Description

This 12-lesson unit contains lessons on dilations and similarity. Dilations are performed both in the Euclidean and coordinate planes. Similarity is defined in terms of transformations using dilations. Properties of similar figures and specifically similar triangles are proven and then used to establish facts about partitioning, the medians of triangles, and right triangles. Finally, similarity is used to prove the Pythagorean Theorem.

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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.

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Geometry Homework, Lesson Plans and Worksheets

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THE BIG IDEA

Being able to establish similarity in geometric shapes allows us to determine angles and establish ratios for corresponding sides. Similar triangles help us to establish how parallel lines partition segments proportionally. These early theorems become very useful in establishing even more concepts as the year develops.

TRAPS & PITFALLS

One classic issue appears EVERY YEAR is comparing the proportional pieces cut by the parallel line to the 3rd side that has not been cut into pieces. Students too often relate pieces of sides to whole sides and that causes an error.

PAST CONNECTIONS

The connection to things before this of course is similarity. Any connections to ratios, scale factors, proportion, etc... all connect to the concept of similarity and the non-isometric transformation, dilation.

FUTURE CONNECTIONS

Parallel lines, proportional relationships, and congruent angles unlock many problems in the future. These new proven theorems will allow students to go at larger problems and have a logical structure to explain why it works.

MY REFLECTIONS (over line l )

The ‘Side Splitting Theorem’, as I have come to know it, where a parallel line to a side of a triangle cuts the other two sides into proportional parts causes students some trouble.  They handle the easy relationships of comparing pieces to pieces but when the ratio of the full length side is used in a ratio they often compare the wrong things.  Do lots of these problems to work out this issue. 

The proof of the angle bisector theorem is a nice proof and a nice use of similarity but it is a pretty useless fact, I can’t think of a time in geometry that it gets used except in its own specific question type.

Finally, the proof of the Pythagorean Theorem using similarity is quite helpful and beautiful. It leads us nicely into the geometric mean relationship.

Chapter 9, Lesson 4: Compositions of Transformations

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7th Grade Common Core: 7.G.4

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Math Expressions Grade 4 Unit 7 Lesson 4 Answer Key Equivalent Fractions Using Multiplication

Solve the questions in Math Expressions Grade 4 Homework and Remembering Answer Key Unit 7 Lesson 4 Answer Key Equivalent Fractions Using Multiplication to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-4-unit-7-lesson-4-answer-key/

Math Expressions Common Core Grade 4 Unit 7 Lesson 4 Answer Key Equivalent Fractions Using Multiplication

Math Expressions Grade 4 Unit 7 Lesson 4 Homework

Use the fraction strips to show how each pair is equivalent.

Explanation: To make an equivalent pair of fraction multiply numerator and denominator with 3 So, \(\frac{3}{4}\) = \(\frac{9}{12}\)

Explanation: To make an equivalent pair of fraction multiply numerator and denominator with 2 So, \(\frac{2}{5}\) = \(\frac{4}{10}\)

Explanation: To make an equivalent pair of fraction multiply numerator and denominator with 3 So, \(\frac{2}{4}\) = \(\frac{6}{12}\)

Complete to show how the fractions are equivalent.

Explanation: To make an equivalent pair of fraction multiply numerator and denominator with 7 So, \(\frac{5}{6}\) = \(\frac{35}{42}\)

Explanation: To make an equivalent pair of fraction multiply numerator and denominator with 10 So, \(\frac{4}{10}\) = \(\frac{40}{100}\)

Explanation: To make an equivalent pair of fraction multiply numerator and denominator with 9 So, \(\frac{4}{5}\) = \(\frac{36}{45}\)

Explanation: To make an equivalent pair of fraction multiply numerator and denominator with 8 So, \(\frac{2}{5}\) = \(\frac{16}{40}\)

Explanation: To make an equivalent pair of fraction multiply numerator and denominator with 6 So, \(\frac{3}{8}\) = \(\frac{18}{48}\)

Math Expressions Grade 4 Unit 7 Lesson 4 Remembering

Solve. Then explain the meaning of the remainder.

Question 1. Doris is putting together gift bags. She has 53 favors to divide evenly among gift bags for 7 guests. How many favors will each guest get? Answer: 53 ÷ 7 = 49 + Remainder 4

63 ÷ 7 = 9  favors will get each guest Solve each problem.

Question 2. 2 × 9 + 5 = r Answer: 23 Explanation: r = 2 x 9 + 5 r = 18 + 5 r = 23

Question 3. 36 ÷ (20 – 8) = t Answer: 3 Explanation: t = 36 ÷ (20 – 8) t = 36 ÷ 12 t = 3

Question 4. Mattie and Leah each bought an ice cream cone for the same price. Mattie said it cost her \(\frac{2}{3}\) of her allowance. Leah said it cost her \(\frac{1}{3}\) of her allowance. Who gets more allowance? Explain. Answer: Mattie gets more allowance

\(\frac{2}{3}\) > \(\frac{1}{3}\)

Explanation:

\(\frac{2}{3}\) > \(\frac{1}{3}\) Multiply with 9 on both sides \(\frac{2}{3}\) x 9 > \(\frac{1}{3}\) x 9 \(\frac{18}{3}\) > \(\frac{9}{3}\) 6 > 3

Question 5. Stretch Your Thinking Omar cuts a pizza into 4 slices and takes 3 of the slices. He says that he would have the same amount of pizza if he cut the pizza into 8 slices and takes 6 of the slices. Paul says he can cut the pizza into 16 slices and take 12 slices to have the same amount. Who is correct? Explain. Answer: Both are correct, all the fractions are equal Explanation: \(\frac{3}{4}\) = \(\frac{3}{4}\) x \(\frac{2}{2}\) = \(\frac{6}{8}\)

\(\frac{3}{4}\) = \(\frac{3}{4}\) x \(\frac{4}{4}\) = \(\frac{12}{16}\)

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