Honors Geometry Fall Semester Study Guide Mathematician ____ _ _ ___ _______________ Pd . ___

All work must be shown in a neat and organized manner.

1. The measure of an angle is 5 times it’s complement. Find the measure of the angle and it’s supplement.

2. M is the midpoint of. If CM = 5x + 2y, CX =46, and MX =9x –y. Find the value of x and y.

3. The three undefined terms in geometry are ________, ________, and ________. The word “geometry”

means _____________________.

4. Find the slope of the line passing through A (-8,6) and B (4, -12).

5. Find the distance between points (6, 8) and (4, -6). Remember to be able to simplify radicals!

6. Find the coordinates of the midpoint of if R is (-5, 8) and W (12, -2).

7. The midpoint of is (-7, 8). K has the coordinate (5, -1). Find the coordinates of T.

8. Write the equation of the line in slope intercept form with slope 5 and y-intercept 1.345.

9. Use point slope to write the equation of the line parallel to 4x + 3y = 12 containing the point (12, -2).

10. Use point slope to write the equation of the line containing ( 3, 12) and (4, -6). State answer in slope intercept form.

11. Use point slope to write the equation of the altitude from A to if A (-4,2), R(3,9) and T(10,5).

12. Identify the conclusion in the following statement: “If Johnny is bad, then Santa will leave coal in his stocking.”

13. Write the contrapositive of the statement “John will eat brussel sprouts only if he can have dessert with dinner.”

14. Write the inverse of the statement “If it is not foggy, then Santa will find his way.”

15. Provide a counterexample for the statement “If two angles are complementary, then they are congruent.”

16. The five parts of a two-column proof are :

a.________________________ b._____________________c.________________________ d._____________________ e.________________________

17. When writing a proof, the types of items that may be used to support statements are :

_________________, ___________________, __________________, _________________, & _________________.

18. Two points determine a ___________________ while three noncollinear points determine a _________________________. Every line contains at least __________________ points and every plane contains ____________ _______________ ___________________points.

19. Use the statement , to write 6 congruence statements.

_________, ________, __________, ___________, __________, _______

20. The lengths of 2 sides of a triangle are 15 and 8. Write an inequality that represents the length of the third side.

21. D ABC is a right triangle with a right angle at B. mDA = 8x + 9 and mDC = 6x + 11. Find mDC.

22. D is in the interior of . Solve for x if , , and . Are either of your solutions extraneous?

23. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w -1, and RT = 18. Find the length of RS.

25. If an obtuse angle is bisected, the resulting angles will be ____________.

26. P is between R and S. RP = 20 –x and RS = 4x. Express PS in terms of x.

27. SV = 8, PQ = 3x – 5y, TV = 15x + 10y, PR = 20 USE PICTURE TO RIGHT à

x = ____, y = _____________

28. If P lies in the interior of DRST, DRSP = 40°, and mDTSP =60°, then mDRST = _____.

29. Through any two distinct points there exists only _________ line. ____________ angles are formed whenever the sides of two angles form two pairs of opposite rays. If two ___________________ lines are perpendicular to the same line, then they are ______________________________________________.

30. Write the equation of the line perpendicular to 6x – 2y = 9 and containing (-12, 7).

31. Decide if the lines are parallel, perpendicular, or neither.

a. L1 (-10, 9) & (-9, 15) where L2 (1, -4) & (-5, -3)

b. L1 (-10, 9) & (-9, 15) where L2 (1, -4) & (2, 2)

c. L1 (-10, 9) & (-9, 15) where L2 (1, -4) & (2, 3)

32. Is it possible to have a triangle with the sides 4, 6, 10? 3, 5, 9? 5, 5.1, 10?

33. The sides of a triangle are AB = 5x + 4, BC = 2x + 6, and AC = 52. If AB + BC > AC, write an inequality that represents the value of x.

34. In DABC, classify the following as true or false:

a. ____________AC = BC

b. ____________mDA > mDACB

c. ____________ is an altitude of D ABC.

35. The measures of three angles of a triangle are mDA =x + 16, mDB= x + 20, and mDC=2x. Find the measure of each angle. State the longest side.

36. The perimeter of a triangle is 99. AB = 5x + 3, AC = 8x + 2, and BC = 13x -10. Find the length of each side. AB = ___________, AC = __________, BC = ____________. Which angle is the smallest angle? _________________

37. Find the value of x.

Why are the following triangles congruent?


3 8. Given m<BCA = m<DCA ________

4 1. _______

3 9. ________

42. _______

40. Given m<TSR = m<TUR _________

43. If Q is the midpoint of RS and PT, then D PQR @ D SQT by ____________.


44. x = ________ y = ________

45. If m1 m2, l1 l2 then classify the following as true or false:

a. ____ D2 @ D5

b. ____ D3 @ D5

c, _____D2 supplementary D6

d. _____D1 @ D 3

Classify e. ___________ D1 and D4

f. __________D6 and D5

g.____________D3 and D5

Write the converse, inverse and contrapositive of the statement. Determine if each is true or false. If false, give a counterexample.

46. If an angle is acute, then it has a measure greater than 0 and less than 90.

Name the special line segments and the point of concurrency for each of the following:

47. 48. 49. 50.

51. Find the range for the 3rd side given two sides of 10 and 8.

52. mDABC ____ mDDBC 53. ST ______ UV

M is the centroid. Find the following

Classify the following triangles as obtuse, right, or acute.

57. 4, 7, 9 58. 5, 12, 13 59. 4, 6, 7


60. Identify the type of angles

<3 & <7 ___________________________

<4 & <6 ___________________________

<2 & <8 ___________________________

<1 & <8 ___________________________

Using the picture to the left,

Given the lines ║

61. Given m<1 = 4x + 8 m<5 = 6x ─2

Find x __________________

62. Given: m<2 = 11x ─ 5 m<7 = 6x + 15

Find m<7 _____________________

63 . Given m<7 = 7x + 15 m<1 = 9x + 3

Find m<1______________________



Classify the following triangles

64 . 4, 7, 9

65 . 5, 12, 13

66 . 4, 6, 7

6 7. x

3

6

8

6 8. x

y

6 9. x

y

7 0.

7 1. 5 15

x

7 2. 8 x

15

7 3.

x


Proofs

74. Given: P is the midpoint of and .

Prove:

75. Given: T is the midpoint of .

Prove:

76. Given: ║

Prove: <1 and <4 are supplementary

B 4 C

2 3

E 1 F

77. Given: l ║ m; m<1 = m<2

Prove: m<2 = m<4

l 1 2

m 4 3