Download geometry fall final review packet!!

Geometry Fall Final 2015 Review
Name:_______________________________________ Hour:_________
1. Name the ray in the Afigure.
B
2. If T is the midpoint of
find the values of x and ST. The diagram is not drawn to scale.
Show all your algebra!! S
T
U
8x
5x + 24
3. If m∠BOC = 32 and m∠AOC = 53 , then what is the measure of ∠AOB ? The diagram is not
to scale. Please show your arithmetic!!
4. How are the two angles related?
5. Find the value of x. Don’t forget to show all work!
6. Find the values of x and y. Show all your algebra!!
Be sure to answer all parts of the question!!
3y°
2x + 3°
111°
Drawing not to scale
7. The sum of the measures of two exterior angles of a triangle is 215. Find the measure of
the third.
8. Find the value of x for v to be parallel to u. Diagram is not to scale. 9.
10.
11.
12. State the 5 postulates that are used to prove triangles are congruent.
13. State which postulate is used to prove these triangles are congruent.
14. Solve for x and y 15. Solve for x, y, and z. 16. Solve for x. 17. Solve for x.
18. Identify what each of the drawn segments are in the marked triangles.
A
B
C
D
19. In the given figure, G is a centroid. Find the following if….
a. If AE = 18, FE =
E
C
D
B
G
b. If GD = 5, AG =
c. If CF = 21, CG =
E
A
F
20. Write the angles in order from smallest to largest.
21. Two sides of a triangle have sides 12 and 7. The length of the third side must be greater than
less than
? .
22. Identify the following by name:
AD=
EB =
CF=
?
and
23. In parallelogram BQEA, 𝐴𝑂 = 12𝑥 − 3
and 𝑄𝑂 = 9𝑥 + 6. What is the value of x?
24. Classify quadrilateral ABCD by its most precise name.
25. Find the value of x in the isosceles trapezoid below.
x -3
7x + 1
6x + 9
26. In the kite below, find the value of
∠2 .
2
78°
27. In parallelogram ABCD, find the value of x.
20 – x
3x + 8
28. In the parallelogram below, angle a = 68°. What is the value of angle d?
29. Simplify the following radical:
72
30. Find the slope through the following pair of points: (-12, 15) and (-12, 17)
31. Use the distance formula to find the distance between the points (-3, 0) and (-3, 6)
32. Given rectangle ABCD, which theorem is proved by the following 2-column proof?
Statements 1. Rectangle ABCD 2. AB ≅ DC and AD ≅ BC 3. < DAB and < ABC are right angles 4. < DAB ≅< ABC 5. ABD ≅ BAC 6. AC ≅ BD Reasons 1. Given 2. Opposite sides of a parallelogram are congruent 3. A rectangle has 4 right angles 4. Right angles are congruent 5. SAS 6. CPCTC A) Diagonals of a rectangle are congruent
B) Diagonals of a parallelogram bisect each other
C) Opposite sides of a parallelogram are congruent
D) Opposite angles of a parallelogram are equal
33. Given: ABCD is a parallelogram with AB ≅ BD
Prove: ABCD is a rhombus
Which corresponding reason justifies the stated conclusion?
A) Opposite sides of a parallelogram are congruent?
B) A quadrilateral with 2 congruent adjacent sides is a rhombus
C) Opposite angles of a rhombus are congruent
D) The diagonals of a parallelogram bisect each other.
34. When proving that a quadrilateral is a parallelogram by using distances, you must find:
A) the slopes of all 4 sides
B) the slopes of two opposite sides
C) the lengths of all four sides
D) both the lengths and slopes of all four sides
35. In quadrilateral PNWS below, sides PS and NW are parallel for what values of x.
36. In the figure below, A, B, C, and D are collinear, FC is parallel to ED, BE is perpendicular to ED, and the
measures of FAB and EBA are as marked. What is the measure of <FCB ?
37. In ∆ABC, the sum measures of
A and
B is 112 degrees. What is the measure of
C?
38. The sides of a square are 4.5 cm long. One vertex of the square is at (-1, 0) on a square coordinate grid
marked in centimeter units. State possible points that also be a vertex of a square?
39. Find the value of x. The diagram is not to scale.
40. The two triangles below are congruent, list six things you know are true about the two triangles.
41. State the definition of a trapezoid.
42. If point (-3, 4) is reflected across the x-axis, what is its new coordinate?
If point (-3, 4) is reflected across the y-axis, what is its new coordinate?
43. Please complete the proof.
Given: ∠A ≅ ∠E ; AB ≅
Prove: ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐷𝐶
DE
44. Provide the reason for the proof.