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Understanding Triangle Formation and Geometry Problems

This document covers a variety of mathematical problems involving triangles, line equations, and geometric calculations. It includes questions about triangle formation, similar triangles, the area of squares and triangles, and properties of right triangles. Additionally, it addresses trigonometric functions, including tangent and cosine, and geometric properties such as slopes and angles. Solutions require algebraic manipulation and simplified radical forms. Perfect for students looking to reinforce their understanding of geometry and trigonometry in a structured manner.

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Understanding Triangle Formation and Geometry Problems

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Presentation Transcript

  1. ROUND 1

  2. 1. Which of the following can NOT form a triangle? I. 3, 4, 5 II. 3, 4, 7 III. 3, 4, 10

  3. 2. Given ΔLMN~ ΔTUV, find x. M T x 4 8 12 L N V U 20

  4. 3. What is the area of the square? 5x+4 ft

  5. 4. A right triangle has a hypotenuse of 9 and a leg with length 6. What is the length of the other leg (in simplified radical form)?

  6. 5. What is the length of AC in the triangle? A 10 30° C B

  7. 6. What is the area of a square whose diagonal has a length of in?

  8. ROUND 2

  9. 1. Give the equation of a line that is perpendicular to the line 2x-3y=12

  10. 2. Plot A(0,6), B(2,0) and C(4,0). Find the area of the triangle.

  11. 3. If tan(x)=4/3, what is cos(x)? x

  12. 4. If the probability of winning a game is 4/13, what is the probability of losing the game?

  13. 5. In ΔLMN, LM=15 cm, m<L=90°, and MN=40. To the nearest degree, what is m<N?

  14. 6. How long is the line segment connecting the points (-1,4) and (3,-2)? Please leave your answer as a simplified radical.

  15. ROUND 3

  16. 1. Solve the following equation. Leave your answer in simplified radical form.

  17. 2. Draw ΔDEF with m<D=110°, DE=5, and DF=2. How long is EF, rounded to the nearest hundredth?

  18. 3. If the slope angle of a line has tan(θ)=2/5 and goes through the point (8,6), what is the equation of the line?

  19. 4. Solve the equation:

  20. 5.Find the area of an equilateral triangle with an altitude of 9in. Please leave your answer in simplified radical form.

  21. What is my Dog’s Name?

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