Semester Study Guide
Geometry Study Guide – Chapter 1
Name ______
Use the figure at right to answer problems 1-4.
1. Name a line that contains point D.
2. Name a plane containing lines p and n.
3. Name 3 points coplanar with point A.
Use the figure at right to answer problems 5-6.
4. Name 3 collinear points.
5. Find the value of the variable and RT if S is between R and T.
6. Find the length of the segment between the following endpoints: C, D.
7. Find the coordinates for the midpoint, Y, of if X and Z
Use the figure at right to answer problems 12-13.
and are opposite rays, bisects , and bisects .
8. If and , find the value of x.
9. The measures of two complementary angles are and . Find the value of x and the measure of the angles.
Use the figure at right to answer problems 15-17.
10. Name a pair of vertical angles.
11. Name a linear pair.
12. Find the value of x if .
Chapter 2 Study Guide
13. Make a conjecture about the next term in the sequence. Write the conjecture and state the next term.
- b.
14. Write a conjecture about each value or geometric relationship.
a. and form a linear pair.b. The product of two even numbers.
15. Determine whether each conjecture is true or false. Give a counterexample for any false conjectures.
b. If is between and , then is the midpoint of .
16. Use the following statements to write a compound statement for each conjunction or disjunction. Then find its truth value. Explain your reasoning.
a. ~q v r
b. p ^ ~r
c. ~p^ ~r
17. Determine the hypothesis and conclusion of the statements below.
a. If no sides of a triangle are equal, then it is a scalene triangle.
b. if
18. Write the following statement in if-then form. Then state the hypothesis and conclusion of the conditional statement.
a. If-then form:
b. Hypothesis:
c. Conclusion:
19. Write the converse, inverse, and contrapositive of the true conditional statement. Then determine whether each related conditional is true or false. If a statement is false, find a counterexample.
a. Converse:
b. Inverse:
c. Contrapositive:
20. Determine whether each conclusion is based on inductive or deductive reasoning.
a. At Daisy’s school if you are late five times, you will receive a detention. Daisy has been late to school
five times; therefore she will receive a detention.
b. A dental assistant notices a patient has never been on time for an appointment. She concludes the
patient will be late for her next appointment.
c. A person must have a membership to work out at a gym. Jesse is working out at a gym. Jesse has a
membership to the gym.
21. State the property that justifies each statement.
a. If , then .
b.
c.
22. Given:
Prove:
Chapter 3 Study GuideName
23. Refer to the figure at right to answer each of the following questions.
a. Name all planes parallel to .
b. Name all planes intersecting .
c. Name three segments parallel to .
d. Name three segments skew to .
24. Using the figure at right, name the transversal for each pair of angles and state their special name.
a. and b. and
c. and d. and
25. Use the figure from #2 to complete #3. Given and , solve for the specified angle measure.
a. , find .b. , find .
c. , find .
26. Use the figure from problem #2 to complete #4. Name which lines, if any, are parallel based on the given information. If possible, state the postulate or theorem you used. If given a pair of angles in which you can solve for x, then do so.
a. b.
e. If and , find the value of x.
27. Determine whether and are parallel, perpendicular, or neither. Find the slope of AB and CD and compare
a.
b.
c.
28. Write an equation in slope-intercept form given the following characteristics. Y = MX + B . Need to know point-slope form y – y1 = m( x – x1 ) then use algebra to put in slope intercept form
a. and contains the point b. a line containing the points and
c. a line that passes through and is parallel to the line .
d. a line that contains the point and is perpendicular to the line .
Chapter 4 Study Guide
29. Classify each triangle below by its sides and angles. Sides can be classified as: scalene, isosceles, and/or equilateral. Angles can be classified as: acute, obtuse, right, and/or equiangular.
a.b.c.
Sides: ______Sides: ______Sides:______
Angles: ______Angles: ______Angles: ______
30. Find x and the length of each side if is an isosceles triangle with base .
31. Find the measure of each.
a.b.
c.d.
X = ______
32. If , find the value of x and y.
33. For each problem below, state if the two triangles are congruent by ASA, SAS, SSS, AAS, HL, or Not Possible. If possible, write the congruence statement. Be sure to mark the triangles with any information used to prove congruence.
a.b.
c. d.
e.f.
34. Find each measure.
a. b. c.
9. Solve for the value of x and y. (Note: Don’t panic if your answer(s) are decimal(s)/fraction(s)!)
a.b.
35. Name the missing coordinates of each triangle.
a. b.
Geometry Study Guide – Chapter 9 Name ______
36. has vertices . Graph the triangle and its image based on the transformation given. ONLY WRITE THE COORDINATES OF !
a. Reflection in b. Translation along
c. Rotation about the origind. Rotation about the origin
37. has vertices . Graph the triangle and its image after the composition of transformations in the order listed. WRITE THE COORDINATES OF AND !
a. Rotation about the originb. Translation along
Reflection in Reflection in
Geometry Chapter 5 Study Guide
Name the Theorem that will go with each special segments.
(a) Perpendicular Bisector: ______(b) Angle Bisector: ______
(c) Median: ______(d) Altitude: ORTHOCENTER
38. If P is the circumcenter of , answer the following questions.
(a) If BP = 13, find CP ______and AP______.
(b) If AS = 5, find SC ______.
(c) Using the answers from (a) and (b), find PS.
39. If A is an incenter (which means that PK, QU, and PT are angle bisectors – you have to know this for the test), answer the following questions.
((a) Solve for x.(b) Find
((c) If AK = 8, find AT and AU.(d) Find
(e) Find(f) Find
40. WY is a median, XW = 4x – 3, WZ = 2x + 7, XY = x + 9, and ZY = 2x – 3. Find the value of x and XY.
41. If H is the centroid of , answer the following questions:
(a) If SM = 24, find SH and HM
(b) If RH = 12, find HE and RE
(c) If HD = 3, find HT and TD
42. WY is an altitude, answer the following questions.
WY and XZ form a 90 degree angle.
(a) If , find the value of x.
43. Name the angles and sides from smallest to largest.
Angles: ______, ______, ______
Sides: ______, ______, ______
44. Name the sides and angles from largest to smallest.
Sides: ______, ______, ______
Angles: ______, ______, ______
45 – 46: Determine whether the given measures can be the lengths of the sides of a triangle.
Write yes or no. Explain (Show your work)
45. 5.7, 6.2, 10.946. 2, 3, 5
47 – 48. The measures of two sides of a triangle are given. If the third side is ‘x’, find the range for the value of x.
47. 15 and 2448. 1.5 and 6.5
49: Determine the relationship between the lengths of the given sides for each figure.