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Warm Up

Warm Up. Assessment 2 Geometry Answers. Warm Up # 1. “If a quadrilateral has four equal sides, then that quadrilateral is a square.” Draw me a counterexample to the statement above? Which of the following best describes the triangle below? Are they congruent? Similar?. 35°. 6. 6. 35°.

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Warm Up

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  1. Warm Up Assessment 2 Geometry Answers

  2. Warm Up # 1 • “If a quadrilateral has four equal sides, then that quadrilateral is a square.” Draw me a counterexample to the statement above? • Which of the following best describes the triangle below? Are they congruent? Similar? 35° 6 6 35° 3 3

  3. Warm Up # 1B • Draw me 3 shapes that are similar but NOT congruent? • Are these shape Similar? Congruent? a. b. c. d.

  4. 4 7 ? Warm Up #2 • A triangle has sides with lengths of 4 and 7 inches. Which of the following could be the perimeter of the triangle? • A triangle has sides with lengths of 7 and 10 inches. Which of the following could be the perimeter of the triangle? 3. A triangle has sides with lengths of 11 and 17 inches. Which of the following could be the perimeter of the triangle?

  5. 3 7 ? Warm Up #2B • A triangle has sides with lengths of 3 and 7 inches. Which of the following could be the perimeter of the triangle? • A triangle has sides with lengths of 6 and 10 inches. Which of the following could be the perimeter of the triangle? 3. A triangle has sides with lengths of 10 and 17 inches. Which of the following could be the perimeter of the triangle?

  6. 6x + 43 3x + 43 4x + 43 x + 55 5x + 60 5x + 13 8x + 13 5x + 15 Warm Up # 3 • What is the length of a side of the square below? a. b. c. d.

  7. E B A C D F Warm Up # 3B • In the triangles below, AB=DF and BC=EF. What additional information would be enough to prove that triangle ABC and DEF are congruent?

  8. Warm Up # 4 • In the figure below, • If JK = LM, what will prove that JKL and JML are congruent? b. If JM = KL, what will prove that JKL and JML are congruent? J K 1 3 2 4 M L

  9. K J L M Warm Up # 4B • In the figure below, KL = JM. What postulate or theorem could be used to prove triangle JKL =LMJ?

  10. Warm Up # 5 • A right triangle has legs of lengths 6 and 9. What is the length of the hypotenuse? • A right triangle has legs of lengths 8 and 12. What is the length of the hypotenuse? • A right triangle has legs of lengths 4 and 7. What is the length of the hypotenuse? • A right triangle has legs of lengths 11 and 13. What is the length of the hypotenuse?

  11. Warm Up #5B • Which of the following statements would prove that ABCD is a rhombus? • What type of triangle is formed by the points A(2, 3), B(2, -3) and C(5, 0)? • What type of triangle is formed by the points A(–1, -1), B(2, -3) and C(5, 0)? • What type of triangle is formed by the points A(0, 5), B(2, 0) and C(0, 0)?

  12. Warm Up #5C • If we have a parallelogram EFGH. Which of the following statements would prove that EFGH is a rhombus? Draw a Parallelogram, then a rhombus. • What type of triangle is formed by the points A(2, 4), B(2, -4) and C(5, 0)? • What type of triangle is formed by the points A(–1, -1), B(1, -3) and C(5, 0)? • What type of triangle is formed by the points A(0, 5), B(4, 0) and C(0, 0)?

  13. G 1 J F 3 2 5 4 H 6 K Warm Up # 6 • What additional information will be sufficient to prove that triangle GFH and JFK are similar? Remember we just need 2 angle to be congruent to have 2 similar triangles.

  14. N Y M X O Z Warm Up # 6B In the triangle below, XY = MN and <X = < M. • Which additional information would be sufficient to prove that both triangle are congruent? • Which additional information would NOT be sufficient prove both triangle are congruent?

  15. 5 25 26 ? ? ? 3 7 10 Warm Up # 7 • A fence built around a field has the dimensions shown below. • What is the approximate length of the entire fence? a. b. c.

  16. Warm Up # 7B • What values of x and y make quadrilateral EFGH a parallelogram? Hint : Opposite sides are congruent. a. b. 3x + 4y x – y E E F F 2 26 4x + y -x + 2y 4 24 H H G G

  17. Warm Up # 7C • What values of x and y make quadrilateral EFGH a parallelogram? Hint : Opposite sides are congruent. a. b. 3x + 6 x + y E E F F 2 9 2x + 3y x + 2y 4 7y H H G G

  18. Warm Up # 8 If EFGH is a rhombus, solve for z? a. b. (3, 4) (x, y) E E F F (3+z, 4) (x+z, y) H H (z,0) (z,0) (0,0) (0,0) G G

  19. Warm Up # 8B If EFGH is a rhombus, solve for z? Then find Slope for FH and EG? Then multiply FH and EG. a. What do you notice about FH and EG? (3, 4) E F (3+z, 4) H (z,0) (0,0) G

  20. Warm Up # 8C If EFGH is a rhombus, solve for z? Then find Slope for FH and EG? Then multiply FH and EG. a. What do you notice about FH and EG? (5, 12) E F (5+z, 12) H (z,0) (0,0) G

  21. Warm Up # 9 If EFGH is a parallelogram, what are the coordinates of point E? a. b. (?, ?) (?, ?) E E F F (6, 4) (y, z) H H (x,0) (5,0) (0,0) (0,0) G G

  22. Warm Up # 9B • Which of the following facts would prove that EFGH and LMNO are similar? Hint: What should the ratio be for FG/MO, HG/NO ? What should <H and <G be congruent to ? If we have 2 parallel lines would it help? Which two? 6 F E 115 105 L 2 M 105 9 115 3 N O H G

  23. Warm Up # 10 Page 227 • Make a segment AB. • Put the tip of the compass on point A. • Open the pencil(with compass) tip so that it extend past point B. Then Draw an Arc. • Without adjusting the width of the compass, place the tip on point B and draw an arc that intersects the first arc at point C. • Draw a line segment from point A to C and from point B to C.

  24. Warm Up # 10B Page 271 • On a triangle ABC. Put the tip of the compass on to point B. • Open the pencil (with compass) tip so that it not pass segment AC. Draw an arc. Label the intersection on BC point K and on AB point M. • Without adjusting the width of the compass. Place the tip on point K and draw an arc. Same with point M. • Where both arc intersects call it point H. • Lastly, make segment BH and that is the altitude.

  25. Warm-Up 10 C: Page 545: Pythagorean Theorem Proof. x • Find the area for Triangle x. • Find the area for Triangle y. • Find the area for Triangle z. • Find the area of x , y , z. • Find area of the trapezoid. • Find sum for triangle x, y, z. • Does answer number 6 have the same answer as number 5? 22 y 4 5 3 5 4 3 z

  26. Warm-Up 10 D: Page 545: Pythagorean Theorem Proof. x • Find the area for Triangle x. • Find the area for Triangle y. • Find the area for Triangle z. • Find the area of x , y , z. • Find area of the trapezoid. • Find sum for triangle x, y, z. • What happens when the Answer of problem 5 is equal to Answer of problem 6? 22 y j m k m k j z

  27. Warm Up # 11 • Which of the following is not an undefined term use in geometry? • Triangle b. point c. line d. plane • Which of the following statements represents deductive reasoning? • Using logic to draw conclusions based on accepted statements. • Recognizing pattern in weather, then making a prediction based upon that pattern. • Singing “Yankee Doodle Dandy” to yourself. • Clark Gable • Which of the following statements represents inductive reasoning? • Using logic to draw conclusions based on accepted statements. • Recognizing a pattern in weather, then making a prediction based upon that pattern. • Reciting a Dr. Seus phrase to your neighbor. • Elvis Grabac.

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