Geo Chapters 7-9 Review

Geo Chapters 7-9 Review

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1. The coin shown is in the shape of an 11-gon. Find the sum of the measures of the interior angles.

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2. Find m∠S in the diagram.

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3. A convex hexagon has exterior angles with measures 34°, 49°, 58°, 67°, and 75°. What is the measure of an exterior angle at the sixth vertex?

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4. Find the values of x and y. Write your answer as "x, y"

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5. Find the value of b.

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6. For what value of x is quadrilateral MNPQ a parallelogram?

Multiple Choice

7. State which theorem you can use to show that the quadrilateral is a parallelogram.

• Parallelogram Opposite Sides Converse

• Parallelogram Opposite Angles Converse

• Parallelogram Diagonals Converse

• Opposite Sides Parallel and Congruent Converse

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9. Find the measure of ∠1 in rhombus DEFG.

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10. QS = 4x − 15 and RT = 3x + 8. Find the lengths of the diagonals of rectangle QRST.

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11. Find the measure of ∠R n the isosceles trapezoid.

Multiple Choice

12. Is quadrilateral VWXY an isosceles trapezoid?

• Yes, because there is one pair of parallel sides.

• No, because the diagonals do not bisect each other.

• No, because the diagonals are not congruent.

• Yes, because there is one pair of parallel sides and base angles are congruent.

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13. Find AB.

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14. Find m∠G.

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15. Find KM.

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16. The two gazebos shown are similar pentagons. Find the perimeter of Gazebo A.

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17. In the diagram, GHJK ∼ LMNP. Find the area of LMNP.

Multiple Choice

19. Can you prove that △CDF and △DEF are similar?

• Yes, by AA Similarity Theorem

• Yes, by SAS Similarity Theorem

• Yes, by SSS Similarity Theorem

• No, there is not enough information.

Multiple Choice

20. Which of the three triangles are similar? Write a similarity statement.

• △YZX ∼ △RST

• △RST ∼ △LMN

• △LMN ∼ △YZX

Multiple Choice

21. Can you prove that △SRT ∼ △PNQ?

• Yes, by AA Similarity Theorem

• Yes, by SSS Similarity Theorem

• Yes, by SAS Similarity Theorem

• No, there is not enough information.

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22. Find the length of  $\overline{YZ}$ . Round to the nearest tenth.

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23. Find the value of the x.

Multiple Choice

24. Tell whether the triangle is a right triangle.

• yes

• no

Multiple Choice

25. Verify that segments with lengths of 4.1, 8.2, and 12.2 form a triangle. Is the triangle acute, right, or obtuse?

• Acute

• Right

• Obtuse

• Does not form a triangle.

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27. Find the value of x. Write your answer in simplest form.

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28. Find the values of x and y. Write your answers in simplest form. Write your answer as "x, y".

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29. Find the geometric mean of 18 and 54. Round to the nearest tenth.

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30. Find the value of x. Round to the nearest tenth.

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31. Find the value of x. Round your answer to the nearest tenth.

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32. Find the value of x. Round to the nearest tenth.

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33. Find the value of y. Round to the nearest tenth.

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34. Find m∠D. Round decimal answers to the nearest tenth.

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35. Find the area of the triangle. Round your answer to the nearest tenth.

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36. Find m∠C. Round decimal answers to the nearest tenth.

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37. Find CB. Round to the nearest tenth.