Transcript Quarterly 2 Test Review

Quarterly 2 Test
Review
For #1-5, choose the method used to prove the
triangles congruent. HL SAS AAS SSS ASA
1.
A and D are right ’s; 𝐴𝐵 ≅ 𝐵𝐷
HL Thm
2.
𝐴𝐵 ≅ 𝐵𝐷; 𝐴𝐶 ≅ 𝐶𝐷
SSS Post.
3.
A and D are right angles; 𝐴𝐵 ≅ 𝐷𝐸
AAS Thm
4.
C is the midpoint of 𝐵𝐷 and 𝐴𝐸
SAS Post.
5.
𝐶𝐵 bisects ACD; 𝐶𝐵 ⊥ 𝐴𝐷
ASA Post.
6. Complete the following proof by filling in the missing reasons.
Given: ∠B ≅ ∠ C; M is the midpoint of 𝐵𝐶
Prove: 𝐴𝐵 ≅ 𝐷𝐶
STATEMENTS
REASONS
2. M is the midpoint of 𝐵𝐶
Given
Given
2.______________________
3. 𝐵𝑀 ≅ 𝐶𝑀
Def. of midpoint
3.______________________
4. ∠AMB ≅ ∠CMD
Vertical ∠’s are ≅.
4.______________________
5. ∆AMB ≅ ∆DMC
ASA Postulate
5.______________________
6. 𝐴𝐵 ≅ 𝐷𝐶
CPCTC
6.______________________
1. ∠B ≅ ∠ C
1. ______________________
7. In an isosceles ABC, 𝐵𝐶 is the base and
m∠B = 42°. Find m∠A and m∠C.
A
B
42°
42°
m∠C = 42°
m∠A = 96°
C
8. If two parallel lines are cut by a transversal, then
≅
corresponding angles are ____________.
9. If two parallel lines are cut by a transversal, then
≅
alternate interior angles are _________.
10. If two parallel lines are cut by a transversal,
supplementary
then same-side interior angles are _____________.
11. A median of a triangle is a segment from the
midpoint
vertex to the ________________
of the
opposite side.
altitude
12. A(n) ___________
of a triangle is a segment
from a vertex perpendicular to the opposite
side.
13. A perpendicular bisector of a segment is a
perpendicular
line (or ray or segment) that is ______________
midpoint
to the segment as its ______________.
For #14-18, answer with always, sometimes, or never.
never 65°.
14. If ΔABC is equiangular, then m∠B is __________
always
15. In any triangle, there is ______________
at least two
acute angles.
16. If two parallel lines are cut by a transversal, then
always congruent.
corresponding angles are __________
sometimes right.
17. If a triangle is isosceles, then it is ____________
always
18. The acute angles of a right triangle are __________
complementary.
For #19 and 20, answer with true or false.
19. A triangle may have the sides measuring 12,
28, 40.
FALSE; 12 + 28 = 40
20. In right triangle ABC, If m∠A = 90°, then 𝐴𝐶
is the longest side.
B
FALSE
A
C
21. Find x.
3x + 85 = 8x
85 = 5x
x = 17
22. What is the interior angle sum of a decagon?
(n – 2)180 (10 – 2)180
1440°
23. What is the exterior angle sum of a decagon?
360°
24. What is the measure of each interior angle of a
regular decagon?
𝑛 −2 180
144°
int ∠ =
𝑛
25. What is the measure of each exterior angle of a
360
regular decagon?
ext. ∠ =
𝑛
36°
26. What polygon has an interior angle measuring
135°?
𝑛 −2 180
octagon
int ∠ =
𝑛
27. List the angles from greatest to smallest.
∠D, ∠F, ∠E
28. List the sides from greatest to smallest.
𝑀𝑂, 𝑁𝑂, 𝑀𝑁
29. If point O lies in the interior of ABC, then
OBC
mABC = mABO + m____________.
A
(hint: Draw your own picture.)
O
B
C
30. If point O does not lie on straight angle ABC,
180
then mABO + mCBO = _____°.
(hint: Draw your own picture.)
O
A
B
C
31. In the diagram, 𝐴𝐶 ⊥ 𝐵𝐷, m∠DBE = (x – 8)°
and m∠EBC = (3x + 2)°. Find x.
3x + 2
x – 8 + 3x + 2 = 90
4x – 6 = 90
4x = 96
x = 24
For # 32 – 35, name the property is used.
32. If a = b and b = c, then a = c.
Transitive Property
33. If a = b, then b = a.
Symmetric Property
34. a = a
Reflexive Property
35. If a = b and a + c = d, then b + c = d.
Substitution Property
36. If two lines intersect, then their intersection
point
is a ______________.
37. If two planes intersect, then their
line
intersection is a ______________.
38. If m∠ROS = (6x + 3)° and m∠TOP = (8x - 7)°,
5
then x = ____.
8x – 7 = 6x + 3
x=5
39. X is the midpoint of 𝑊𝑍. If WX = (3x), XZ =
(x + 6), then find x.
x+6
3x
3x = x + 6
2x = 6
x=3
For #40 - 46, a || b and m∠1 = 75°.
corresponding angles.
40. ∠1 and ∠5 are _______________
s-s interior
41. ∠2 and ∠6 are _______________
angles.
alt. interior
42. ∠5 and ∠6 are _______________
angles.
105°
43. m∠2 = ________
105°
44. m∠3 = ________
75°
45. m∠5 = ________
75°
46. m∠5 = (6x + 2)° and m∠6 = (8x – 10)°. Find x.
6x + 2 = 8x – 10
12 = 2x
x=6
47. What is the image of P(3, –5) using the
translation (x, y) → (x + 4, y – 6)?
P’(3 + 4, –5 – 6)
P’(7, –11)
For #48-51, use the coordinate plane to the right.
48. What is the image of P(1, 4) if (x, y) is
reflected in the y–axis?
P’(–1, 4)
49. What is the image of P(1, 4) if (x, y) is
reflected in the x-axis?
P’(1, –4)
50. What is the image of P(1, 4) if (x, y) is
reflected in the line y = x?
P’(4, 1)
51. What is the image of P(1, 4) if (x, y) is
reflected in the line y = –x?
P’(–4, –1)
For #52 – 54, describe the transformation
shown.
52.
translation
(x, y) → (x + 2, y – 8)
53.
reflection over x-axis
54.
rotation
about the origin
180° clockwise or
counterclockwise
STUDY