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Geometry 1 Final Exam Preview

Geometry 1 Final Exam Preview.

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Geometry 1 Final Exam Preview

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  1. Geometry 1 Final Exam Preview

  2. Mary drew 3 cards from a standard deck of cards (4 suits of 13 cards each) and drew the 4 of hearts, the 4 of clubs and the 4 of diamonds. Abe claimed the deck must be a trick deck as Mary should not have been able to randomly draw three 4’s in a row. Mary claimed there was actually a very slim chance (.018%) that she could draw three 4’s in a row, so it was possible for the deck to be fair. • Who made a statistical argument?

  3. Make a conjecture about the next item in the sequence and then state whether you used inductive or deductive reasoning. 2000 , 1000 , 500 , 250

  4. Identify a counter example to the statement that all months have at least 30 days.

  5. Write the converse, inverse and contrapositive of the given statement and determine if they are true or false. • If a mathematical statement is proven true, then it is a theorem.

  6. Determine the value of a and LM if M is between L and N and LM = 8a, MN= 12a and LN = 190.

  7. Make a truth table for ~p ~q

  8. Make a truth table for ~(p and q)

  9. Write the negation of the given statement, “All linear pairs are supplementary.”

  10. Given the true statement, “If 2 angles form a linear pair, then they are supplementary”. Which is the sufficient condition for the statement?

  11. In the proof of the statement, “If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent,” what is the given?

  12. Determine the length of each side given the perimeter of the rectangle is 108 miles.

  13. You have a piece of string that is 83 centimeters long. If you enclose a square region, how many square centimeters will you enclose?

  14. Determine the coordinates of the midpoint of if Q(1, -3) and R(11, 5).

  15. Determine the length of if Q(1, -3) and R(11, 5).

  16. Name all segments parallel to GFA.

  17. l ∠1 ∠2 m • In the diagram below (not drawn to scale), l//m, m∠1 = 4x – 4 and m∠2 = 7x - 40. Determine the value of x and the measures of each angle. G1.1.2

  18. In the diagram below (not drawn to scale), p//q, m∠3 = 12x - 28 and m∠4 = 4x + 4. Determine the value of x and the measures of ∠3 and ∠4. G1.1.1 and G1.1.2 ∠3 p ∠4 q

  19. Determine the slope of the line parallel to the line 4x + 7y = 17 in the standard (x,y) coordinate plane.

  20. 8x - 2 3x + 13 Given the following information, determine the value of x which guarantees the lines will be parallel.

  21. Triangle ABC is an isosceles right triangle with right angle, ∠B. If AB = 24, how long is the hypotenuse?

  22. The measures of 2 complementary angles are 6x + 2 and 8x -24. What are the measures of the angles?

  23. Name the congruent angles and sides for the pair of congruent triangles. • ∆ ANG ≅ ∆HYU

  24. Refer to the figure. The 3 triangles are all isosceles triangles. What is mRAM? 70 33

  25. Refer to the figure. The 3 triangles are all isosceles triangles. What is m∠XAM? 70° 33°

  26. Refer to the figure. The 3 triangles are all isosceles triangles. If m∠FXA = 116, what is m∠FMX? 70° 33°

  27. Refer to the figure. The 3 triangles are all isosceles triangles. If m∠FXA = 116, what is m∠XFM? 70° 33°

  28. Triangle FJH is an equilateral triangle. Find x and y. H 20y - 16 7x + 4 J 12y + 8 F

  29. Refer to the figure shown. Given the information below, write a congruence statement and state a postulate or theorem that justifies your statement. B A C D E

  30. Refer to the figure shown. Given the information below, write a triangle congruence statement and state a postulate or theorem that justifies your statement. W X V Z Y

  31. Determine the values of x and the measures of ∠A, ∠B and ∠C in the diagram below B 3x + 18 5x -2 C A

  32. Determine the value of y in the figure below 6y + 8 10y 5y - 21

  33. What are the 3 undefined terms in geometry?

  34. B Given: ΔABC with exterior ∠BCD Prove: m∠BCD = m∠A + m∠B A C D

  35. Use the coordinates of ΔABC below to determine if the triangle is equilateral, isosceles or scalene. A(5,6), B(1,2) and C(2,8)

  36. t u HG s G J F • Lines s, t and u are perpendicular bisectors of ΔFGH and meet at J. If JG = 7x + 3 and JH = 9x – 3, determine the value of JF.

  37. Given: ΔABC is equilateral • Prove: ∠ABC is an acute angle • Write an indirect proof.

  38. Draw and label 2 right triangles that could be proven congruent by LL.

  39. Construct an angle congruent to angle B below and then bisect each angle. B

  40. Construct a line through P that is perpendicular to m. P m

  41. Given: ABCD is a parallelogram Prove: ∠A ≅ ∠C B A D C

  42. Given: BD and AE bisect each other Prove: AB = DE D A E C B

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