unit overview - hillsborough county public · pdf filegeometry honors: similarity and...

Geometry Honors: Similarity and Trigonometry Semester 1, Unit 3: Activity 17
Resources:
SpringBoard-
Geometry
Online
Resources:
Springboard
Geometry
Unit 3 Vocabulary
Dilation Center of Dilation Similarity Transformation Similar Indirect Measurement Triangle Proportionality
Theorem Parallel Proportionality
Theorem Right Angle Altitude
Theorem Geometric Mean Pythagorean Theorem Pythagorean Triple Opposite Leg Adjacent Leg Trigonometric Ratio Sine Cosine Tangent Inverse Trigonometric
Function Law of Sines Law of Cosines Triangulation
Unit Overview
In this unit, students will study special right triangles and right triangle trigonometry. You will also study similarity transformations and similarity in polygons.
Student Focus
Main Ideas for success in lessons 17-1, 17-2, and 17-3:
Perform dilations on and off the coordinate plane.
Describe dilations.
Understand the meaning of similarity transformations.
Use similarity transformations to determine whether figures are similar.
Identify properties of similar figures.
Apply properties of similar figures.
Page 1 of 41
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Example 17-1:
A graphic artist has enlarged a rectangular photograph using a scale factor of
4. The perimeter of the enlargement is 144 in. What is the perimeter of the original photograph?
36 in.
A photographer enlarged a picture. If the width of the image is 5 inches and
the width of the pre-image was x, what is the scale factor for the dilation In terms of x?
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Example 17-2:
Use geometry software or grid paper to perform the following compositions
of transformations on the pre-image.
Pre-image:
Page 3 of 41

Example 17-3:
Find the missing side length for the pair of similar figures.
Page 4 of 41

Resources:
SpringBoard-
Geometry
Online Resources:
Springboard
Geometry
Unit 3 Vocabulary
Unit Overview
In this unit, students will study special right triangles and right triangle trigonometry. You will also study similarity transformations and similarity in polygons.
Student Focus
Main Ideas for success in lessons 18-1, 18-2, and 18-3:
Develop criteria for triangle similarity.
Prove the AA similarity criterion.
Show triangles are similar.
Use similar triangles to solve problems.
Prove the Triangle Proportionality Theorem and its converse.
Apply the Triangle Proportionality theorem and its converse.
Page 5 of 41

Example 18-1:
For each pair of triangles, write which similarity criterion, if any, can be used to show the triangles are similar.
AA similarity
SAS or SSS similarity
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Example 18-2:
Determine if the pair of triangles is similar. If so, write the similarity criterion that can be used to show they are similar and find the unknown measure.
RQ = ___________
Yes; by the SAS Similarity Theorem; RQ 42.7
Page 7 of 41

Example 18-3:
Given the diagram, determine whether the segments are parallel. Show your work.
BJ and CH
No;
Page 8 of 41

Resources:
SpringBoard-
Geometry
Online Resources:
Springboard
Geometry
Unit 3 Vocabulary
Unit Overview
In this unit, students will study special right triangles and right triangle
trigonometry. You will also study similarity transformations and
similarity in polygons.
Student Focus
Main Ideas for success in lessons 19-1 and 19-2:
Identify the relationships that exist when an altitude is drawn to the
hypotenuse of a right triangle.
Prove the Right Triangle Altitude Theorem.
Apply the relationships that exist when an altitude is drawn to the
hypotenuse of a right triangle.
Page 9 of 41

Example 19-1:
In the figure, is a right triangle and is an altitude to the hypotenuse. Suppose you know
that . What other angle in the figure must also measure 62? Why?
Example 19-2:
Find the geometric mean of 2.5 and 9.1. Write in radical
form.
Page 10 of 41

Resources:
SpringBoard-
Geometry
Online Resources:
Springboard
Geometry
Unit 3 Vocabulary
Unit Overview
Student Focus
Use similar triangles to prove the Pythagorean Theorem.
Apply the Pythagorean Theorem to solve problems.
Use the converse of the Pythagorean Theorem to solve problems.
Develop and apply Pythagorean inequalities.
Page 11 of 41

Example 20-1:
One of the diagonals of a rectangle measures 15 cm.
The width of the rectangle is 6 cm. Determine the
perimeter of the rectangle.
Length = cm
Perimeter = 2(13.7 + 6) = 39.4 cm
Example 20-2:
Tell whether the triangle having the following side
lengths can be formed. If the triangle can be formed,
tell whether it is right, acute, or obtuse.
36, 77, 85
Right
22, 18, 3
Cannot be the sides of a triangle
Page 12 of 41

Resources:
SpringBoard-
Geometry
Online Resources:
Springboard
Geometry
Unit 3 Vocabulary
Unit Overview
Student Focus
Describe the relationships among the side lengths of 45 - 45 - 90
triangles.
Apply relationships in special right triangles to solve problems.
Describe the relationships among the side lengths of 30 - 60 - 90
triangles.
Apply relationships in special right triangles to solve problems.
Page 13 of 41

Example 21-1:
For each 45 -45 -90 triangle, find a and b. Write all
answers in simplest radical form.
a = 3
b =
Example 21-2:
Find the perimeter of .
60 +
Page 14 of 41

Resources:
SpringBoard-
Geometry
Online Resources:
Springboard
Geometry
Unit 3 Vocabulary
Unit Overview
trigonometry. You will also study simi

unit overview - hillsborough county public · pdf filegeometry honors: similarity and...

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