Geometry 7-4 Similarity in Right Triangles

by Matthew Richardson

| 27 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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10 pts

Solve It! Draw a diagonal of a rectangular piece of paper to form two right triangles. In one triangle, draw the altitude from the right angle to the hypotenuse. Number the angles as shown. Cut out the three triangles.

How can you match the angles of the triangles to show that all three triangles are similar?

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10 pts

Solve It! Explain how you know the matching angles are congruent.

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Problem 1 Got It?

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Problem 1 Got It?

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10 pts

Problem 2 Got It?

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10 pts

Problem 3 Got It?

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10 pts

Problem 4 Got It? From point D, the robot must turn right and move to point B to put the bottle in the recycling bin. How many inches does the robot travel from D to B? Enter only the number.

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10 pts

What is the geometeric mean of 4 and 9?

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10 pts

What is the geometric mean of 4 and 12?

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Vocabulary: Classify the segments of △RST. Sides may have more than one classification.

- segment RP
- segment RT
- segment TP

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

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10 pts

Error Analysis: A classmate wrote an incorrect proportion to find x. Explain and correct the error.

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Review Lesson 7-3: Write a similarity statement for the two triangles.

△RMN ~ △PNQ

△RMN ~ △NQP

△NMR ~ △QPN

△NRM ~ △NPQ

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10 pts

Review Lesson 7-3: How do you know the triangles are similar?

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10 pts

Review Lesson 6-2: Algebra: Find the value of x in ▱RSTV.

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Review Lesson 6-2: Algebra: Find the value of y in ▱RSTV.

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10 pts

Review Lesson 7-2: Enter only the value of x.

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Review Lesson 7-2: Enter only the value of x.

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Review Lesson 7-2: Enter only the value of x. Round to the nearest hundredth.

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Vocabulary Review: Complete each sentence with the correct word from the list.

- parallel
- perpendicular
- congruent
- isosceles

- 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.

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10 pts

Vocabulary Review: Identify the altitude of △ABC.

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10 pts

Use Your Vocabulary: Which proportion can you use to find the geometric mean of 5 and 15?

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15 pts

Use Your Vocabulary: Complete the items on the canvas.

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10 pts

Reflection: Math Success

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