Geometry Unit 7 Note Sheets

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Ratios and Proportions Notes Vocabulary: Ratio _____________________________________________________________________________________

Extended Ratio _____________________________________________________________________________

Guided Practice

1. One ounce of cheddar cheese contains 9 grams of fat. Six of the grams of fat are saturated fats. Find the ratio of saturated fat to total fat in an ounce of cheese.

Your Turn

2. The number of students that participate in sports at Central High school is 520. The total number of students in the school is 1850. Find the athlete to student ratio to the nearest tenth.

Guided Practice

3. The ratio of the measures of the angles in triangle ABC is 3: 4: 5. Find the measures of the angles. Your Turn

4. The ratios of the measures of the sides of a triangle is 6:7:9, and it’s perimeter is 77 centimeters. Find the measure of each side of the triangle.

Geometry Unit 7 Note Sheets

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Vocabulary

Proportion ________________________________________________________________________________

Extremes _________________________________________________________________________________

Means ____________________________________________________________________________________

Cross Product ______________________________________________________________________________

Cross Product Property

Guided Practice Solve each proportion.

5. 𝑥𝑥+32

= 4𝑥𝑥5

6. 𝑥𝑥12

= 5𝑥𝑥

Your Turn 7. 4𝑥𝑥−53

= −266

8. 6𝑦𝑦

= 𝑦𝑦15

Guided Practice

9. 7𝑥𝑥−2

= 9𝑥𝑥+4

10. 𝑥𝑥4

= 10𝑥𝑥

Your Turn

11. 𝑥𝑥+2𝑥𝑥−2

= 32 12. 8

𝑥𝑥= 𝑥𝑥

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Geometry Unit 7 Note Sheets

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Dilations Notes

Guided Practice

1. Use a ruler to draw the image of triangle ABC under a dilation with center D and scale factor of 12.

Your Turn

2. Use a ruler to draw the image of the figure under a dilation with center J and scale factor of 32.

Geometry Unit 7 Note Sheets

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Guided Practice 3. Quadrilateral 𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽 has the vertices 𝐽𝐽(−2, 4), 𝐽𝐽(−2,−2), 𝐽𝐽(−4,−2), and 𝐽𝐽(−4, 2). Graph the image of 𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽 after a dilation centered at the origin with a scale factor of 2.5. Your Turn 4. Trapezoid 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 has vertices 𝐸𝐸(−8, 4), 𝐸𝐸(−4, 8), 𝐸𝐸(8, 4), and 𝐸𝐸(−4,−8). Graph the image 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 after

dialation centered around the origin with scale factor of 14.

Geometry Unit 7 Note Sheets

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Similar Polygons Notes

Guided Practice 1. Vocabulary Scale factor ________________________________________________________________________________ Guided Practice 2. Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not explain your reasoning.

Geometry Unit 7 Note Sheets

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Your Turn 3. Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not explain your reasoning.

Guided Practice In the diagram, 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐸𝐸~𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅. 4. Find 𝑥𝑥. Your Turn 5. Find 𝑦𝑦.

Guided Practice Your Turn 6. 7.

Geometry Unit 7 Note Sheets

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Similar Triangles Notes Angle-Angle (AA) Similarity

Guided Practice Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. 1. Your Turn 2. Side-Side-Side (SSS) Similarity

Side-Angle-Side (SAS) Similarity

Reflexive Property of Similarity

Symmetric Property of Similarity

Transitive Property of Similarity

Geometry Unit 7 Note Sheets

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Guided Practice Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning. 3. 4. Your Turn 5. 6. Guided Practice Your Turn 7. Find WR and RT. 8.

Geometry Unit 7 Note Sheets

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Parts of Similar Triangles Notes Special Segments of Similar Triangles

Guided Practice 1. In the figure ∆𝐴𝐴𝐴𝐴𝐴𝐴~∆𝐸𝐸𝐴𝐴𝐸𝐸. Find the value of x. 2. Find the value of x.

Your Turn 3. 4.

Geometry Unit 7 Note Sheets

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Guided Practice Your Turn 5. 6. Triangle Angle Bisector

Guided Practice Find x. 7. 8. Your Turn 9. Find x. 10.

Geometry Unit 7 Note Sheets

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Parallel Lines and Proportional Parts Notes Triangle Proportionality Theorem

Guided Practice Your Turn 1. In ∆𝑃𝑃𝑃𝑃𝑅𝑅, 𝑅𝑅𝑅𝑅 ∥ 𝑅𝑅𝑃𝑃. If 𝑃𝑃𝑅𝑅 = 7.5, 2. 𝑅𝑅𝑃𝑃 = 3, and 𝑅𝑅𝑅𝑅 = 2.5, find 𝑃𝑃𝑅𝑅. Converse of Triangle Proportionality Theorem

Guided Practice Your Turn 3. 4.

Geometry Unit 7 Note Sheets

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Vocabulary Midsegment of a Triangle ____________________________________________________________________ Triangle Midsegment Theorem

Guided Practice In the figure, 𝑋𝑋𝑋𝑋 and 𝑋𝑋𝑌𝑌 are midsegments of ∆𝑅𝑅𝑅𝑅𝑅𝑅. Find the measure of 𝑋𝑋𝑌𝑌, 𝑅𝑅𝑅𝑅, and 𝑚𝑚∠𝑅𝑅𝑋𝑋𝑋𝑋. 5. 𝑋𝑋𝑌𝑌 6. 𝑅𝑅𝑅𝑅 7. 𝑚𝑚∠𝑅𝑅𝑋𝑋𝑋𝑋 Your Turn 8. 𝐴𝐴𝐴𝐴 9. 𝐸𝐸𝐸𝐸 10. 𝑚𝑚∠𝐴𝐴𝐸𝐸𝐸𝐸