geometry unit 7 note sheets ratios and proportions notes...
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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.
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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