Name: _______________________________________________
Ch 5-6 Review Worksheet
Period: __________________
Determine the coordinates of each translated image without graphing.
1. The vertices of parallelogram HJKL are
units up to form parallelogram
,
,
, and
. Translate the parallelogram 7
.
2. The vertices of quadrilateral WXYZ are
the right and 8 units down to form quadrilateral
, and Z (3, 7). Translate the quadrilateral 5 units to
.
Determine the coordinates of each rotated image without graphing.
3. The vertices of triangle RST are R (0, 3), S (2, 7), and
counterclockwise to form triangle
.
4. The vertices of quadrilateral WXYZ are
origin
counterclockwise to form quadrilateral
. Rotate the triangle about the origin
, and Z (3, 7). Rotate the quadrilateral about the
.
Determine the coordinates of each reflected image without graphing.
5. The vertices of triangle RST are R (0, 3), S (2, 7), and
.
6. The vertices of quadrilateral WXYZ are
axis to form quadrilateral
.
. Reflect the triangle over the x-axis to form triangle
, and Z (3, 7). Reflect the quadrilateral over the y-
7. Identify the transformation used to create
on each coordinate plane. Identify the congruent angles and the
congruent sides. Then, write a triangle congruence statement.
7.
List the corresponding sides and angles, using congruence symbols, for each pair of triangles represented by the
given congruence statement.
8.
9.
Determine whether each pair of given triangles are congruent. Use the Distance Formula and a protractor when
necessary.
10.
Congruent by SSS?
11.
Congruent by SAS?
Determine the angle measure or side measure that is needed in order to prove that each set of triangles are
congruent by SAS.
12. In
, and
. In
, and
.
13. In
, and
. In
, and
.
14.
15.
Determine whether there is enough information to prove that each pair of triangles are congruent by SSS or
SAS. Write the congruence statements to justify your reasoning.
16.
17.
18.
19.
20.
21.
22.
23.
Determine the angle measure or side measure that is needed in order to prove that each set of triangles are
congruent by ASA.
24. In
, and
. In
, and
.
25. In
, and
. In
, and
26.
27.
28.
29.
.
30. Determine whether
31.
Determine whether
by AAS.
is congruent to
by ASA.
is congruent to
32.
Determine whether
by AAS.
is congruent to
Determine the angle measure or side measure that is needed in order to prove that each set of triangles are
congruent by AAS.
33. In
, and
. In
, and
.
34. In
, and
. In
, and
35.
36.
37.
38.
.
Determine whether there is
enough information to prove that each pair of triangles are congruent by ASA or AAS. Write the congruence
statements to justify your reasoning.
39.
40.
41.
42.
43.
44.
45.
46.
Mark the appropriate sides to make each congruence statement true by the Hypotenuse-Leg Congruence
Theorem.
47.
48.
Mark the appropriate sides to make each congruence statement true by the Leg-Leg Congruence Theorem.
50.
49.
Mark the appropriate sides and angles to make each congruence statement true by the Hypotenuse-Angle
Congruence Theorem.
52.
51.
Mark the appropriate sides and angles to make each congruence statement true by the Leg-Angle Congruence
Theorem.
53.
54.
Create a two-column proof to prove each statement.
55. Given:
Prove:
56. Samantha is hiking through the forest and she comes upon a canyon. She wants to know how wide the canyon is. She
measures the distance between points A and B to be 35 feet. Then, she measures the distance between points B and C to
be 35 feet. Finally, she measures the distance between points C and D to be 80 feet. How wide is the canyon? Explain.
57.
Explain why
.
58.
Calculate MR given that the perimeter of
is 60 centimeters.
Determine the value of x in each isosceles triangle.
59.
60.
61.
62.
63.
64.
65. A kaleidoscope is a cylinder with mirrors inside and an assortment of loose colored beads. When a person looks
through the kaleidoscope, different colored shapes and patterns are created as the kaleidoscope is rotated. Suppose that
the diagram represents the shapes that a person sees when they look into the kaleidoscope. Triangle AEI is an isosceles
triangle with
bisects
and
bisects
. What is the length of , if one half the length of
is 14 centimeters? Explain.
Write the converse of each conditional statement. Then, determine whether the converse is true.
66. If the lengths of the sides of a triangle are 3 cm, 4 cm, and 5 cm, then the triangle is a right triangle.
67. If the corresponding sides of two triangles are congruent, then the triangles are congruent.
68. If the corresponding angles of two triangles are congruent, then the triangles are similar.
Write the inverse of each conditional statement. Then, determine whether the inverse is true.
69. If two angles are complementary, then the sum of their measures is
.
70. If a polygon is a square, then it is a rhombus.
71. If a polygon is a trapezoid, then it is a quadrilateral.
Write the contrapositive of each conditional statement. Then, determine whether the contrapositive is true.
72. If two angles are supplementary, then the sum of their measures is
.
73. If the radius of a circle is 8 meters, then the diameter of the circle is 16 meters.
74. If the diameter of a circle is 12 inches, then the radius of the circle is 6 inches.
For each pair of triangles, use the Hinge Theorem or its converse to write a conclusion using an inequality,
75.
76.
ch 5-6 review worksheet
Answer Section
1. ANS:
The vertices of parallelogram
PTS: 1
REF: 5.1
TOP: Skills Practice
2. ANS:
The vertices of quadrilateral
are
,
,
, and
.
NAT: G.CO.2 | G.CO.3 | G.CO.5
are
,
,
, and
PTS: 1
REF: 5.1
TOP: Skills Practice
3. ANS:
The vertices of triangle
are
NAT: G.CO.2 | G.CO.3 | G.CO.5
PTS: 1
REF: 5.1
TOP: Skills Practice
4. ANS:
The vertices of quadrilateral
NAT: G.CO.2 | G.CO.3 | G.CO.5
, and
.
are
, and
PTS: 1
REF: 5.1
TOP: Skills Practice
5. ANS:
The vertices of triangle
are
NAT: G.CO.2 | G.CO.3 | G.CO.5
PTS: 1
REF: 5.1
TOP: Skills Practice
6. ANS:
The vertices of quadrilateral
NAT: G.CO.2 | G.CO.3 | G.CO.5
, and
are
.
.
.
, and
PTS: 1
REF: 5.1
NAT: G.CO.2 | G.CO.3 | G.CO.5
TOP: Skills Practice
7. ANS:
Triangle BND was translated 10 units to the right to create triangle XYZ.
PTS: 1
REF: 5.2
TOP: Skills Practice
8. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8
PTS: 1
REF: 5.2
TOP: Skills Practice
9. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8
.
PTS: 1
REF: 5.2
TOP: Skills Practice
10. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8
The triangles are not congruent.
PTS: 1
REF: 5.3
TOP: Skills Practice
11. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Side-Side Congruence Theorem
The triangles are congruent by the SAS Congruence Theorem.
PTS: 1
REF: 5.4
TOP: Skills Practice
12. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
PTS: 1
REF: 5.4
TOP: Skills Practice
13. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
PTS: 1
REF: 5.4
TOP: Skills Practice
14. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
PTS: 1
REF: 5.4
TOP: Skills Practice
15. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
PTS: 1
REF: 5.4
TOP: Skills Practice
16. ANS:
The triangles are congruent by SSS.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
PTS: 1
REF: 5.4
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
TOP: Skills Practice
KEY: Side-Angle-Side Congruent Theorem
17. ANS:
There is not enough information to determine whether the triangles are congruent by SSS or SAS. SAS
does not apply because the congruent angles in the figure are not included angles.
PTS: 1
REF: 5.4
TOP: Skills Practice
18. ANS:
The triangles are congruent by SAS.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
PTS: 1
REF: 5.4
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
TOP: Skills Practice
KEY: Side-Angle-Side Congruent Theorem
19. ANS:
There is not enough information to determine whether the triangles are congruent by SSS or SAS. SAS
does not apply because the congruent angles in the figure are not included angles.
PTS: 1
REF: 5.4
TOP: Skills Practice
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
20. ANS:
The triangles are congruent by SAS.
PTS: 1
REF: 5.4
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
TOP: Skills Practice
KEY: Side-Angle-Side Congruent Theorem
21. ANS:
There is not enough information to determine whether the triangles are congruent by SSS or SAS.
PTS: 1
REF: 5.4
TOP: Skills Practice
22. ANS:
The triangles are congruent by SAS.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
PTS: 1
REF: 5.4
TOP: Skills Practice
23. ANS:
The triangles are congruent by SSS.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
PTS: 1
REF: 5.4
TOP: Skills Practice
30. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Side-Angle-Side Congruent Theorem
The triangles are congruent by the ASA Congruence Theorem.
PTS: 1
REF: 5.5
TOP: Skills Practice
24. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Side-Angle Congruence Theorem
PTS: 1
REF: 5.5
TOP: Skills Practice
25. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Side-Angle Congruence Theorem
PTS: 1
REF: 5.5
TOP: Skills Practice
26. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Side-Angle Congruence Theorem
PTS: 1
REF: 5.5
TOP: Skills Practice
27. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Side-Angle Congruence Theorem
PTS: 1
REF: 5.5
TOP: Skills Practice
28. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Side-Angle Congruence Theorem
PTS: 1
REF: 5.5
TOP: Skills Practice
29. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Side-Angle Congruence Theorem
PTS: 1
REF: 5.5
TOP: Skills Practice
31. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Side-Angle Congruence Theorem
The triangles are not congruent.
PTS: 1
REF: 5.6
TOP: Skills Practice
32. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
The triangles are congruent by the AAS Congruence Theorem.
PTS: 1
REF: 5.6
TOP: Skills Practice
33. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
34. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
35. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
36. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
37. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
38. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
39. ANS:
The triangles are congruent by AAS.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
TOP: Skills Practice
KEY: Angle-Angle-Side Congruence Theorem
40. ANS:
There is not enough information to determine whether the triangles are congruent by ASA or AAS.
PTS: 1
REF: 5.6
TOP: Skills Practice
41. ANS:
The triangles are congruent by ASA.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
42. ANS:
The triangles are congruent by AAS.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
TOP: Skills Practice
KEY: Angle-Angle-Side Congruence Theorem
43. ANS:
There is not enough information to determine whether the triangles are congruent by ASA or AAS.
PTS: 1
REF: 5.6
TOP: Skills Practice
44. ANS:
The triangles are congruent by ASA.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
45. ANS:
The triangles are congruent by AAS.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
46. ANS:
The triangles are congruent by ASA.
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 5.6
TOP: Skills Practice
47. ANS:
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12
KEY: Angle-Angle-Side Congruence Theorem
PTS: 1
REF: 6.1
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 |
G.MG.1
TOP: Skills Practice
KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | HypotenuseAngle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem
48. ANS:
PTS: 1
REF: 6.1
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 |
G.MG.1
TOP: Skills Practice
KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | HypotenuseAngle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem
49. ANS:
PTS: 1
REF: 6.1
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 |
G.MG.1
TOP: Skills Practice
KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | HypotenuseAngle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem
50. ANS:
PTS: 1
REF: 6.1
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 |
G.MG.1
TOP: Skills Practice
KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | HypotenuseAngle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem
51. ANS:
PTS: 1
REF: 6.1
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 |
G.MG.1
TOP: Skills Practice
KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | HypotenuseAngle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem
52. ANS:
PTS: 1
REF: 6.1
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 |
G.MG.1
TOP: Skills Practice
KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | HypotenuseAngle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem
53. ANS:
PTS: 1
REF: 6.1
G.MG.1
TOP: Skills Practice
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 |
KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | HypotenuseAngle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem
54. ANS:
PTS: 1
REF: 6.1
NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 |
G.MG.1
TOP: Skills Practice
KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | HypotenuseAngle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem
55. ANS:
Statements
Reasons
1.
1. Given
2.
2. Base Angle Converse Theorem
3.
3. Given
4.
4. Given
5.
5. SSS Congruence Theorem
6.
6. CPCTC
PTS: 1
REF: 6.2
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: corresponding parts of congruent triangles are congruent (CPCTC) | Isosceles Triangle Base Angle
Theorem | Isosceles Triangle Base Angle Converse Theorem
56. ANS:
The canyon is 80 feet wide.
The triangles are congruent by the Leg-Angle Congruence Theorem. Corresponding parts of congruent
triangles are congruent, so
.
PTS: 1
REF: 6.2
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: corresponding parts of congruent triangles are congruent (CPCTC) | Isosceles Triangle Base Angle
Theorem | Isosceles Triangle Base Angle Converse Theorem
57. ANS:
Using
and the Base Angle Theorem,
Theorem,
. Since
and
of the measures of the angles in a triangle is
,
. Using
are supplementary,
.
and the Base Angle
. Since the sum
PTS: 1
REF: 6.2
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: corresponding parts of congruent triangles are congruent (CPCTC) | Isosceles Triangle Base Angle
Theorem | Isosceles Triangle Base Angle Converse Theorem
58. ANS:
cm. Using the Base Angle Converse Theorem,
. Solve the perimeter equation
, where
and
. So,
.
PTS: 1
REF: 6.2
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: corresponding parts of congruent triangles are congruent (CPCTC) | Isosceles Triangle Base Angle
Theorem | Isosceles Triangle Base Angle Converse Theorem
59. ANS:
PTS: 1
REF: 6.3
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem |
Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides
Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem
60. ANS:
PTS: 1
REF: 6.3
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem |
Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides
Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem
61. ANS:
PTS: 1
REF: 6.3
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem |
Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides
Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem
62. ANS:
PTS: 1
REF: 6.3
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem |
Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides
Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem
63. ANS:
PTS: 1
REF: 6.3
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem |
Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides
Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem
64. ANS:
PTS: 1
REF: 6.3
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem |
Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides
Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem
65. ANS:
The length of
is 28 centimeters.
By the Isosceles Triangle Angle Bisector to Congruent Sides Theorem,
and
are congruent. Since
half the length of
is 14 centimeters, its full length is 28 centimeters. Therefore, the length of
is 28
centimeters. So, the length of
is 28 centimeters.
PTS: 1
REF: 6.3
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem |
Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides
Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem
66. ANS:
The converse of the conditional would be:
If a triangle is a right triangle, then the lengths of its sides are 3 cm, 4 cm, and 5 cm.
The converse is not true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
67. ANS:
The converse of the conditional would be:
If two triangles are congruent, then the corresponding sides of the two triangles are congruent.
The converse is true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
68. ANS:
The converse of the conditional would be:
If two triangles are similar, then the corresponding angles of the two triangles are congruent.
The converse is true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
69. ANS:
The inverse of the conditional would be:
If two angles are not complementary, then the sum of their measures is not
.
The inverse is true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
70. ANS:
The inverse of the conditional would be:
If a polygon is not a square, then it is not a rhombus.
The inverse is not true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
71. ANS:
The inverse of the conditional would be:
If a polygon is not a trapezoid, then it is not a quadrilateral.
The inverse is not true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
72. ANS:
The contrapositive of the conditional would be:
If the sum of the measures of two angles is not
, then the angles are not supplementary.
The contrapositive is true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
73. ANS:
The contrapositive of the conditional would be:
If the diameter of a circle is not 16 meters, then the radius of the circle is not 8 meters.
The contrapositive is true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
74. ANS:
The contrapositive of the conditional would be:
If the radius of a circle is not 6 inches, then the diameter of the circle is not 12 inches.
The contrapositive is true.
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
75. ANS:
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem
76. ANS:
PTS: 1
REF: 6.4
NAT: G.CO.10 | G.MG.1
TOP: Skills Practice
KEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem |
Hinge Converse Theorem