Geometry - Chapter 5 QUIZLET Test Review
1. Acute. 2. Isosceles.
10. Triangle EFG, with, 2, sides/lines that are parallel, is which, 2, types of triangles?
1. Scalene. 2. Right.
14. We can tell, by the way, that triangle ABC is which, 2, types of triangles?
Equal to the sum of the measures of the, 2, non-adjacent angles.
23. The measure of an exterior angle of a triangle is ________ to the _________ of the _________________s of the ____, _____-___________________, ___________s.
20
24. A triangle has measures that are, 40, (5x + 15) and (8x - 5) degrees. The value of, x, for this, is ________.
25
25. A triangle has measures that are, 40, 3x and (5x - 10) degrees. The value of, x, for this, is _______.
Polygons, with the same shape, and, size.
26. Congruent polygons are ______________s, with the same ______________, and, __________.
Corresponding angles, and, sides, are also congruent, too.
27. If, for some reason, 2, polygons, are congruent, then, the _____________________________ing, __________s, and, ________s, are also _______________________, too.
2, triangles are congruent iff all corresponding parts of both triangles are congruent.
28. We know that when ____, ______________s are ___________________ iff all __________________________ing, __________s of both ______________________s are _____________________.
Order
29. Also, for this, when writing a congruent statement, corresponding vertices must be listed in the exact, same, ____________.
3
3. An equilateral triangle has ____ congruent sides.
<|SRT =~ <|BCA
30. 2, triangles; triangle SRT and triangle BCA, have, 3, angles, and, lines, that are congruent. So, for that, we can tell, by the way, that <|_________ =~ <|________.
8
31. In a figure, triangle LMN =~ triangle RST. Triangle LMN has measures that are, 24, 63, and, 93, degrees, and, triangle RST has measures that are, 93, 3x and 3x + y degrees. So, for that, we can tell, by the way, that the value of, x, for this, is ____.
Half of both. This is because they are alternate interior angles.
33. For this, can you show that triangle ABD =~ triangle CDB? Showing that all corresponding angles are congruent? Yes, no, or, half of both? Which types of angles are they?
The third angle(s) is/are also congruent.
34. For the Third Angles Theorem, if, 2, angles, of, 1, triangle, are congruent, to, 2, angles, of another triangle, then, the ________, _________(s) is/are also _______________________.
38
35. 2, triangles; triangle ABC and triangle RPO, are both used by the Third Angles Theorem. For this, we have triangle ABC, with angles measuring, 52, and, 90, degrees. For triangle RPO, angle, O, measures, 90, degrees, and, angle, R, measures, 52, degrees. So, for that, we can tell, by the way, that the measure of angle, P, is ________ degrees.
True
4. True or False: When those triangles, described from flashcard, 3 (previous FC), are equilateral, then, all of the angles are congruent.
Base
40. The angles, opposite, the, 2, congruent sides, are the ________ angles.
Isosceles Triangle Theorem
41. All of that information, described from flashcards, 37, 38, 39, and, 40 (the 4 previous FCs before this one), is called the ______________________, _______________, _______________________.
Equiangular
44. For equilateral triangles, we can tell, by the way, that they are, for sure, but, that is, iff it is ___________________________________.
60
46. This is, like, for example, when all, 3, angles are congruent, meaning that they have the same measure. This is, because, 180, divided by, 3, equals, 60, meaning that all, 3, angles, measure ______ degrees.
<HGK =~ <HKG
47. For this, we have, 2, triangles; triangle HGK and triangle HKG. If ___HG =~ ___HK, then, <________ =~ <__________.
___HK =~ ___JK
48. Also, if <KGJ =~ <KJH, then, ___[____] =~ ___[____]. (your answers go in the brackets)
True
5. True or False: Acute triangles have all acute angles.
31
50. Triangle LMN measures, 93, degrees. So, for that, the value of, x, is _______.
30
51. Triangle ZYX measures, 180, degrees. The side length is, 12. All angles measure, 60, degrees, but, because of a 2x showing on angle, Z, the value, of, x, for that, is ________.
15
52. For this, we see an isosceles and an equilateral triangle. For the isosceles triangle, the side length is, 28. The angles measure 2x and, 20, degrees. For the equilateral triangle, the side lengths are 4y and, 28. All, 3, angles of this triangle measure, 60, degrees. So, for that, for the isosceles triangle, the value of, x, is ______.
22
54. Triangle HJG has measures that are 3x and (x + 44) degrees. So, for that, the value of, x, for this, is _______.
70
55. For this, we have, 2, triangles. The first triangle measures, 40, 70, and, 70, degrees. The second triangle measures 2y + 10 and x - y degrees. So, for that, we can tell, by the way, that, for the first triangle, the value of, x, is ______.
1. SAS. 2. SSS. 3. HL. 4. ASA. 5. AAS.
57. For the Triangle Congruence Theorem, what are the, 5, possible theorems for this?
<|ABC =~ <|DEF by SAS
58. This is, like, for example, 2, triangles; triangle ABC and DEF. We can tell, by the way, that <|_______ =~ <|________ by ________.
<|BCA =~ <|EFD by SSS
59. Another example of this is that <|_______ =~ <|________ by _________.
<|DEF =~ <|ABC by HL
60. Another specific example of this is that <|_______ =~ <|__________ by ______.
<|FDE =~ <|CAB by ASA
61. Another specific-ly-er example of this is that <|_______ =~ <|________ by ________.
<|CAB =~ <|FDE by AAS
62. A last example of this is that <|________ =~ <|_________ by __________.
False. It uses HL.
67. True or False: The image shown here shows that triangles YWZ and XZW are congruent by AAS. If you said False, then, tell me, which theorem do these triangles use?
False. It uses AAS.
68. True or False: The image shown here show that triangles CAB and XYZ are congruent by ASA. If you said False, then, tell me, which theorem do these triangles use?
True
69. True or False: The image shown here shows that triangles PQT, RQT, RST, and, PST, are overlapping.
1. First, it's given. 2. Second, it defines the definition of midpoint. 3. Third, it's given, again. 4. Fourth, we can tell, by the way, that all right angles are congruent. 5. Fifth, it uses the Reflexive Property. 6. Last, we can tell, by the way, that both triangles are congruent by SAS.
70. For this, we have, 2, triangles; triangle ABC and triangle DBC. We have, B, as the midpoint of ___AD. Also, <ABC and <DBC are right angles. Now, prove to yourself that <|ABC =~ <|DBC. Explain, in, 6, steps, on how to solve this.
False
1. True or False: Scalene triangles have congruent sides.
10
100 (MAX). On a diagram, DEFG =~ QMNP. DEFG has side lengths that are, 8, and, 12, ft., and has angle measures that are, 68, 84, and, 102, degrees. QMNP has a side length that is (x - 2) ft., and has an angle measure that is (3x + 2y) degrees. So, for that, the value of, x, for this, is _______.
4.2
11. On a graph, triangle ABC is being classified, this is, by its sides. So, we have, A, at, -6, 6, B, at, 9, 3, and, C, at, 2, 2. The distance from point, A, to, point, B, is ____.____.
7.1
12. The distance from point, B, to, point, C, is ____.____.
5.7
13. The distance from point, C, to, point, A, is ____.____.
180
15. For the Triangle Sum Theorem, the sum of the interior angles is _______ degrees. This means, that, we add the measure of angles, A, B, and, C, to get that number.
1. First, it's given. 2. Second, it uses the Angle Addition Postulate. 3. Third, it uses the Alternate Interior Angles Theorem. 4. Last, it uses the Substitution POE.
16. Prove that the measure of angles, 1, 2, and, 3, equal, 180, degrees. For this, triangle ABC has lines BD and AC that are parallel. What are the, 4, steps to solving this?
32
17. A triangle has measures that are, 63, and, 85, degrees. The measure of, x, is _______ degrees.
29
18. A triangle has measures that are, 61, and, 90, degrees. The measure of, x, is _______ degrees.
14
19. A triangle has measures that are 4x and 3x + 20. The value of, x, for this, is ________.
2
2. An isosceles triangle has ____ congruent sides.
Complementary
20. The acute angles of a right triangle are all ________________________________________.
32
21. A triangle has measures that are 2x and (x - 6) degrees. The value of, x, for this, is _______.
26, and, 64
22. The measures of each acute angle are _______, and, __________ degrees.
19
32. The value of, y, is _______.
1. First, it's given. 2. Second, it uses the Third Angles Theorem. 3. Third, it uses the Reflexive Property. 4. Last, we can tell, by the way, that all of the corresponding parts of that triangle are congruent.
36. What are the, 4, steps to prove that triangle ACD is congruent to triangle CAB, when we have these, 2, congruent lines: 1. ___AD =~ ___CB? 2. ___DC =~ ___BA? ... and these, 2, congruent angles: 1. <ACD =~ <CAB? 2. <CAD =~ <ACB?
Legs
37. For an isosceles triangle, the, 2, congruent sides are the ______s.
Base
38. The third side is the _______.
Vertex
39. The, 2, congruent sides form the ____________ angle.
Base angles of an isosceles triangle are also congruent, too.
42. One more thing. For this, we can also tell, by the way, that the ________, ________s of an ____________________, _______________________ are also _______________________, too.
The sides, opposite them, are congruent.
43. For the converse of that theorem, described from flashcards, 37, 38, 39, 40, 41, and, 42 (the 6 previous FCs before this one), we can tell that, if, 2, angles of a triangle are congruent, then, the _______s, ________________ them, are ____________________.
180
45. Equilateral triangles sum adds up to ________ degrees.
1. The first one uses the Isosceles Triangle Theorem. 2. The second one uses the Converse Isosceles Triangle Theorem.
49. For flashcards, 47, and, 48 (the 2 previous FCs before this one), we can tell, by the way, that both of those uses which, 2, theorems?
7
53. For the equilateral triangle, the value of, y, is ____.
20
56. For the second triangle, the value of, y, is ______.
True
6. True or False: Obtuse triangles have all obtuse angles.
False. It uses AAS.
63. True or False: The image shown here shows that triangles HIJ and KML are congruent by SAS. If you said False, then, tell me, which theorem do these triangles use?
False. It uses ASA.
64. True or False: The image shown here shows that triangles BAC and WXY are congruent by SSS. If you said False, then, tell me, which theorem do these triangles use?
Flip triangle XYZ over then put it with triangle ABC.
65. For this, how can we make triangle ABC and XYZ congruent by HL?
True
66. True or False: The image shown here shows that triangles ABC and XYZ are congruent by AAS.
True
7. True or False: Right triangles have only, 1, right angle.
1. First, it's given. 2. Second, it uses the Reflexive Property. 3. Third, it's given, again. 4. Fourth, it defines the definition of perpendicular angles. 5. Fifth, we can tell, by the way, that all right angles are congruent. 6. Last, we can also tell, by the way, that both triangles are congruent by HL. 7. (BONUS STEP) Also, we can tell, by the way, that both triangles are overlapping.
71. For this, we have, 2, triangles; triangle WYZ and triangle XZY. To get us started on this, we first can tell, by the way, that ___WY =~ ___XZ. Also, we can tell that ___WZ is perpendicular to ___ZY, and ___XY is perpendicular to ___ZY. Now, prove to yourself that <|WYZ =~ <|XZY. Explain, in, 6, steps, plus, 1, extra bonus step, on how to solve this.
1. First, it's given. 2. Second, it uses the Reflexive Property. 3. Last, we can tell, by the way, that both triangles are congruent by SSS.
72. For this, we have, 2, triangles; triangle KLM and triangle NLM. To get us started on this, we have lines KL and NL that are parallel to each other, and, we have lines KM and NM that are congruent. Now, prove to yourself that <|KLM =~ <|NLM. Explain, in, 3, steps, on how to solve this.
1. First, it's given. 2. Second, angles, H, and, F, are congruent, and, that's because they are alternate interior angles. 3. Third, angles HED and FEG are congruent, and, that's because they are vertical angles. 4. Fourth, it's given, again. 5. Last, we can tell, by the way, that both triangles are congruent by AAS.
73. For this, we have, 2, triangles; triangle DEH and triangle GEF. To get us started on this, we first have lines DH and FG that are parallel to each other, and, we have lines DE and EG that are congruent. Now, prove to yourself that <|DEH =~ <|GEF. Explain, in, 5, steps, on how to solve this.
1. First, it's given. 2. Second, angles RTS and VTU are congruent, and, that's because they are vertical angles. 3. Third, it's given, again. 4. Last, we can tell, by the way, that both triangles are congruent by AAS.
74. For this, we have, 2, triangles; triangle RST and triangle VTU. To get us started on this, we have angles, S, and, U, that are congruent, and, we also have lines RS and VU that are congruent, too. Now, prove to yourself that <|RST =~ <|VTU. Explain, in, 4, steps, on how to solve this.
1. First, it's given. 2. Second, it defines the definition of perpendicular angles. 3. Third, we can tell, by the way, that all right angles are congruent. 4. Fourth, it's given, again. 5. Fifth, we can tell, by the way, that angles ACB and DCE are congruent, and, that's because they are vertical angles. 6. Last, we can tell, by the way, that both triangles are congruent by ASA.
75. For this, we have, 2, triangles; triangle ABC and triangle DEC. To get us started on this, we have lines AB, AD, and DE (followed by line AD again) that are perpendicular, and we have lines AC and DC that are congruent. Now, prove to yourself that <|ABC =~ <|DEC. Explain, in, 6, steps, on how to solve this.
Corresponding Parts of Congruent Triangles are Congruent
76. CPCTC stands that/for __________________________ing, _______s of __________________, _______________s are ______________________.
Proven that, 2, triangles are congruent, then, you can use this to show that additional sides and angles are (to) also (be) congruent.
77. For this, once, you have __________n that ____, ______________s are __________________, then, you can use this to ________ that ____________________al, _________s and _________s are (to) also (be) _________________________.
1. First, it's given. 2. Second, it's given, again. 3. Third, it uses the Reflexive Property. 4. Last, we can tell, by the way, that both triangles are congruent by AAS.
78. For this, we have, 2, triangles; triangle QRT and triangle SRT. To get us started on this, we have angles RQT, RST, RTQ, and RTS, that are congruent. Now, prove to yourself that ___QT =~ ___ST by CPCTC. Explain, in, 4, steps, on how to solve this.
1. First, it's given. 2. Second, it's given, again. 3. Third, it uses the Reflexive Property. 4. Last, we can tell, by the way, that both triangles are congruent by SSS.
79. For this, we have, 2, triangles; triangle ABD and triangle CBD. To get us started on this, we have lines AD, CD, AB, and CB, that are congruent. Now, prove to yourself that <A =~ <C by CPCTC. Explain, in, 4, steps, on how to solve this.
1. Scalene. 2. Obtuse.
8. Triangle PQR, with, 3, rainbows on angle, Q, is which, 2, types of triangles?
1. First, it's given. 2. Second, it's given, again. 3. Third, it defines the definition of midpoint. 4. Fourth, it uses the Vertical Angles Theorem. 5. Last, we can tell, by the way, that both triangles are congruent by ASA.
80. For this, we have, 2, triangles; triangle NMP and triangle KML. To get us started on this, we have angles, N, and, K, that are congruent, and, we also have, M, as the midpoint of ___NK. Now, prove to yourself that ___LK =~ ___PN by CPCTC. Explain, in, 5, steps, on how to solve this.
1. First, it's given. 2. Second, it's given, again. 3. Third, it uses the Alternate Interior Angles Theorem. 4. Fourth, it uses the Reflexive Property. 5. Last, we can tell, by the way, that both triangles are congruent by AAS.
81. For this, we have, 2, triangles; triangle ADC and triangle DAB. To get us started on this, we have angles, C, and, B, that are congruent, and, we have lines AB and DC that are parallel to each other. Now, prove to yourself that ___AC =~ ___DB by CPCTC. Explain, in, 5, steps, on how to solve this.
Exterior
82. When there is a short line on either the, left, or, right, side of the triangle, we can tell, by the way, that there is a fourth angle. This is called the ___________ angle.
m<1 = m<A + m<B
83. For the Exterior Angles Theorem, we can tell, by the way that the m<____ = m<____ + m<____.
65
84. Looking back from flashcard, 25, we can tell that the exterior angle measures ______ degrees.
1. If ___AB =~ ___BC, then, <A =~ <C. 2. If <D =~ <E, then, ___EF =~ ___DF.
85. Looking back from flashcards, 37, 38, 39, 40, 41, 42, and, 43, for that theorem described there, we know that, in which, 2, examples does it describe these, 2, theorems (one for each): 1. Isosceles Triangle Theorem? 2. The converse of the Isosceles Triangle Theorem?
1. Scalene. 2. Right.
86. A support beam is shaped like a rectangle, with a triangle that goes with it. Its measures are, 35, 55, and, 90, degrees. This is which, 2, types of triangles?
7.3
87. For this, we have to classify triangle ABC, this is, by its sides. Then, we have to determine that if it is a right triangle, or, not. So, we have a triangle on a graph. The points are: 1. A: 0, 3. 2. B: 7, 1. 3. C: 1, -1. The distance from point, A, to, point, B, is ____.____.
4.1
88. The distance from point, A, to, point, C, is ____.____.
6.3
89. The distance from point, B, to, point, C, is ____.____.
1. Scalene. 2. Right.
9. Triangle ABC, with a right angle on angle, C, is which, 2, types of triangles?
-2/7
90. The slope of ___AB is -____/____.
-4
91. The slope of ___AC is -____.
1/3
92. The slope of ___BC is ____/____.
1. Answer, 1: False. 2. Answer, 2: True. 3. Answer, 3: False.
93. Answer these, 3, questions with a True or False: 1. 2, slopes have a product of, -1. 2. No sides are perpendicular to each other at all. 3. There are some right angles. After you choose your, 3, answers, then, check them over. But, make sure that they match, otherwise, if they don't, then, that'll cause you to get it incorrect.
1. Acute. 2. Scalene.
94. Looking back from flashcards, 87, 88, 89, 90, 91, 92, and, 93 (the 7 previous FCs before this one), we can tell, by the way, that triangle ABC is which, 2, types of triangles?
40
95. For this, we have angles, P, Q, R, and, S. The angle measures that we see on this are (3x + 25), 2x, and, 65, degrees. So, for that, the value of, x, is ______.
145
96. Now, we need to find the measure of angle PQS. It is ________ degrees.
36
97. The measure of, 1, acute angle is 1.5 times the measure of the other angle. So, if, it is 1.5 times the measure of the other angle, then, the value of, x, for this, is ________.
36, and, 54
98. The measures of the acute angles are _______, and, _______ degrees.
Congruence Statement: <|MNP =~ <|YXZ. Corresponding Angles: <P =~ <Z, <M =~ <Y, <N =~ <X. Corresponding Sides: ___MN =~ ___YX, ___NP =~ ___XZ, ___PM =~ ___ZY.
99. Write: 1. A congruence statement. 2. Identify all corresponding angles. 3. Identify all corresponding sides. ... for these, 2, triangles: 1. <|MNP. 2. <|YXZ.