Download Geometry_S1_Final Review

NAME: _______________________________________ PERIOD: ________ DATE:_____________
GEOMETRY SEMESTER 1 REVIEW
Use the diagram at the right for Exercises 1.
1. What is the intersection of the two planes?
2.
bisects ABC so that mABD = 2y and mDBC = 5y – 12. What is mDBC?
3. ABC and CBD are supplementary angles. mABC = 8x + 12 and mCBD = 2x + 28.
What is mABC? What is the mCBD?
4. Graph the figure in the coordinate plane and find the PERIMETER.
Coordinate points are: L(0,1), M(3, 5), N(5,5), P(5,1).
1
5.
QR has endpoints Q (9, 2) and R (3, 5). What are the coordinates of its midpoint X?
6. The midpoint of GH is (4, 7). One endpoint is H (12, 3). What are the coordinates of endpoint
G?
7. Identify a pattern and find the next three numbers in the pattern.
a. 5, 10, 20, 40, . . .
b. 5, 8, 11, 14, . . .
c. 3, 1, 1, 3, . . .
d. 1, 3, 6, 10, 15, . . .
8. Determine if the conditional is true or false. If it is false, find a counterexample.
a. If the figure has four congruent angles, then the figure is a square.
b. If an animal barks, then it is a seal.
9. Write the converse, inverse, and contrapositive of the given conditional statement.
a. If two angles are complementary, then their measures sum to 90.
2
b. If a figure is a rectangle, then it has exactly four sides.
10. Is each statement below a good definition? If not, explain.
a. A rectangle is a quadrilateral with four congruent angles.
b. A hexagon is a polygon with exactly six sides.
11. Decide whether the angles are alternate interior angles, same-side interior angles,
corresponding angles, or alternate exterior angles.
a.
2 and 7
b. 5 and 4
c.
8 and 3
d. 6 and 4
e.
1 and 5
12. Find the distance between each pair of points
a. A(6, 7), B(1, 7)
b. C(5, 5), D(5, 3)
c. E(1, 0), F(12, 0)
d. Q(2, 6), T(10, 0)
3
13. Circle the correct answer; show all work on a separate sheet of paper.
Label problems on your separate sheet of paper 13.1 – 13.6.
14. Rewrite each equation in slope intercept form. Then determine whether the lines are parallel.
Explain.
a. 2y = x + 15
b. 10y + 130 = 50x
c. 2y = 15 + 4x
x = 2y + 5
5y = 2x + 11
6y  30 = 12x
4
15. Circle the correct answer; show all work on a separate sheet of paper.
Label problems on your separate sheet of paper 15.1 – 15.6.
16. Given: mABC = 80
DBC = mABC
Angle Addition Postulate
Substitution Property
(3x + 3) + (6x + 5) = 80
a.
9x + 8 = 80
b.
9x = 72
c.
x=8
Angle Addition Postulate
Substitution Property
5
17. Complete the two-column proof.
Given: BD  AB , BD  DE ,
BC  DC
Prove: A  E
Statements
Reasons
1) BD  AB , BD  DE
1)
2) CDE and CBA are right angles.
2) Definition of right angles
3) CDE  CBA
3)
4)
4) Vertical angles are congruent.
5) BC  DC
5)
6)
6)
7) A  E
7)
18. CONSTRUCTION & Complete the two-column proof.
Use a construction to prove that the two base
angles of an isosceles triangle are congruent.
Given: Isosceles ABC with base AC .
Prove: A  C
Statements
Reasons
1) ABC is isosceles.
1)
2) AB  CD
2) Definition of isosceles triangle.
3) Construct the midpoint of AC
and call it D. Construct DB .
4)
3) Construction
5) BD  BD
5)
6) ABD  CBD
6)
7)
7)
4) Definition of midpoint
6
19. Circle the correct answer; show all work on a separate sheet of paper.
Label problems on your separate sheet of paper 19.1 – 19.6.
20.
a. Find MN.
b. Find MQ.
c. Find MP.
d. Find PS.
7
21. Find the value of x:
22. Find the value of x:
8
23. P is the centroid of MNO. MP = 14x + 8y. Write expressions to represent PR and MR.
24. F is the centroid of ACE. AD = 15x2 + 3y. Write expressions to represent AF and FD.
25. Circle the correct answer; show all work on a separate sheet of paper.
Label problems on your separate sheet of paper 25.1 – 25.5.
9
26. Find the sum of the angle measures of each polygon.
27. Algebra Find the missing angle measures.
10
28. For what value of x is the figure the given special parallelogram?
rhombus
rectangle
Use the diagram at the right for Exercises 7 and 8.
29. Two points that are 2 units from T.
30. A segment congruent to QT
11
31. Using the Law of Detachment, what conclusion, if any, can you make from the
two given statements?
Statement 1: If x = 3, then 3x – 4 = 5.
Statement 2: x = 3
a.
b.
c.
d.
3x – 4 = 5
x=3
If 3x – 4 = 5, then x = 3.
not possible
If possible, use the Law of Detachment to make a conclusion. If it is not possible to
make a conclusion, tell why.
32. Using the Law of Detachment, what conclusion, if any, can you make from the
two given statements?
If a triangle is a right triangle, then the triangle has one 90º angle.
ABC is a right triangle.
If possible, use the Law of Syllogism to make a conclusion. If it is not possible to make a
conclusion, tell why.
33. To take Calculus, you must first take Algebra 2.
To take Algebra 2, you must first take Algebra 1.
34. A quadrilateral has four congruent sides if and only if it is a rhombus.
A square is a rhombus.
12
35. Developing Proof Fill in the missing statements or reasons for the two-column proof.
Given: E is the midpoint of DF .
Prove: DE = 23
Statements
Reasons
1) E is the midpoint of DF .
1)
2)
2) Definition of midpoint
3) 6x + 5 = 8x – 1
3)
4) 5 = 2x – 1
4)
5)
5) Addition Property of Equality
6)
7) DE = 6x + 5
8) DE = 6(3) + 5
9) DE = 23
6) Division Property of Equality
7) Given
8)
9)
36. Find the measure of each angle 1 and 2:
13
37. Use the map below to answer these questions:
14