HISET Geometry Flashcards
(185 cards)
1
Q
Point
A
An exact location. It has
no size, only position.
2
Q
Line
A
a straight path that has
no thickness and extends forever
3
Q
Plane
A
a flat surface with no
thickness that extends
forever
4
Q
Segment
A
A part of a line consisting of two endpoints
and all points between
them.
5
Q
Ray
A
a part of a line that
starts at an endpoint
and extends forever in
one direction
6
Q
Endpoint
A
A point at either end of a
line segment, or a point
at one end of a ray.
7
Q
Opposites rays
A
two rays that both start
from a common point
and go off in exactly opposite directions
8
Q
Polygon
A
A closed plane figure
made up of line segments
9
Q
Similar Shapes
A
Have the same shape but not necessarily the same size
- Similar shapes are represented by the symbol ∼
△ABC∼△DEF
10
Q
Congruent
A
Having the same size and shape
- Congruent shapes are represented by the symbol ≅,
△ABC≅△DEF
11
Q
One - Dimensional
A
Having length but no width or height.
12
Q
Two - Dimensional
A
Having length and width.
Having area, but not volume.
Also called a plane figure.
13
Q
Three - Dimensional
A
3-D. Existing in 3 dimensions; having length, width, and height.
14
Q
Which of the following is the difference of similar shapes to congruent shapes?
(A) Similar shapes have the same shape but not necessarily the same size, while congruent shapes have the same shape and the same size.
(B) Similar shapes are scaled versions of each other, while congruent shapes are identical copies of each other.
(C) Both similar shapes and congruent shapes have the same shape and the same size.
(D) Both similar shapes and congruent shapes have the same shape but not necessarily the same size. of the following is the difference of Similar Shapes to congruent shapes? :
A
A
15
Q
Coplanar
A
points that lie on the same plane
16
Q
Collinear
A
points that lie on the same line
17
Q
This is labeled with a lower case letter with 2 points on it
A
Line
18
Q
Which is the following a notation for ? :
↔
AB
A
Line
19
Q
Which is the following a notation for ? :
━
AB
A
Line Segment
20
Q
Which is the following a notation for ? :
→
AB
A
Ray
21
Q
This is labeled with a capital letter
A
Point
22
Q
This is labeled by a script capital letter or 3 points not on the line
A
Plane
23
Q
Axiom
A
a statement that is considered true and does not require proof
24
Q
What is the axiomatic system?
A
a set of axioms used to derive theorems
25
Axioms are what?
basic truths
26
Postulates
Basic truths that do not require formal proofs to prove that they are true
27
Finish the following postulate : A plane contains at least ________________________
three noncollinear points.
28
Finish the following postulate : A line contains at least ____________
two points.
29
Finish the following postulate : Through any two points, there is
exactly one line.
30
Finish the following postulate : Through any three noncollinear points, there is_________________
is exactly one plane.
31
Finish the following postulate : If two points lie in a plane, then___________________
the line joining them lies in that plane.
32
Finish the following postulate : If two planes intersect, then ___________________
their intersection is a line.
33
Finish the following Theorem : If two lines intersect, then ______________________
they intersect in exactly one point.
34
Finish the following Theorem : If a point lies outside a line, then ________________________
exactly one plane contains both the line and the point.
35
Finish the following Theorem : If two lines intersect, then_____________________
exactly one plane contains both lines.
36
Points that lie on the same line are ______________
collinear
37
Points that lie on the same plane are ______________
coplanar
38
A ray has how many endpoints?
1
39
A line segment has how many endpoints?
2
40
All rays start at a point and have a length measurement of _____.
∞ (Infinity)
41
Bisector
The line that divides something into two equal parts.
- Examples of bisector are segment bisector, angle bisector, and shape bisector.
42
Line Segment Bisector
a line, line segment, or ray that intersects a line segment at its midpoint
43
Perpendicular Bisector
a line segment or a ray or a line that intersects a given line segment at a 90 degrees, and also it passes through the midpoint of the line segment.
44
Angle Bisector
a ray that divides an angle into two angles that are congruent
-It creates 2 equal angles
45
How do you solve for the midpoint of a line Segment ?
1. Find the x-coordinate of the midpoint by averaging the x-coordinates of the two endpoints.
2. Find the y-coordinate of the midpoint by averaging the y-coordinates of the two endpoints.
3. The coordinates of the midpoint will be (x-coordinate average, y-coordinate average).
46
Find the midpoint of the line segment with endpoints (2, 3) and (4, 5).
the midpoint is (3, 4)
47
Find the midpoint of the line segment with endpoints (-1, 2) and (5, -4)
the midpoint is (2, -1)
48
A line segment has endpoints at (1, 2) and (7, 8). Find the midpoint of the line segment.
the midpoint is (4, 5)
49
A line segment has endpoints at (-3, -5) and (9, 3). Find the midpoint of the line segment.
the midpoint is (3, -1)
50
Parallel lines
lines in the same plane that never intersect
- Parallel lines are represented by the symbol ∥, such as a∥b.
51
Perpendicular lines
Two lines that intersect to form right angles
- Perpendicular lines are represented by the symbol ⊥, such as a ⊥ b.
52
How do you solve to find out whether a line is parallel or perpendicular?
Determine the slope of each line.
53
How do you determine if two lines are parallel based on their slopes?
If the slopes of the two lines are equal
54
Are vertical lines parallel or perpendicular?
They are considered to be parallel to each other, even though their slopes are undefined.
This is because parallel lines are defined as lines that never intersect, and they never intersect each other.
55
Are horizontal lines parallel or perpendicular?
They are also considered parallel to each other, even though their slopes are 0.
This is because parallel lines are defined as lines that never intersect, and they never intersect each other
56
Explain why vertical lines are perpendicular to horizontal lines.
because they intersect at a 90-degree angle.
57
How do you determine if two lines are perpendicular based on their slopes?
if their slopes are negative reciprocals of each other;
In other words, if the product of the slopes of two lines is -1
58
Determine if the following two lines are parallel , perpendicular or neither:
Line 1: y = 2x + 3
Line 2: y = -2x + 5
The slopes of the two lines are 2 and -2, respectively.
The product of the two slopes is -1, so the lines are perpendicular.
59
Determine if the following two lines are parallel , perpendicular or neither:
Line 1: y = x + 1
Line 2: y = 2x + 2
The slopes of the two lines are 1 and 2, respectively.
The product of the two slopes is not -1, so the lines are neither parallel nor perpendicular.
60
Determine if the following two lines are parallel , perpendicular or neither:
Line 1: y = -3x + 4
Line 2: y = 3x - 2
The slopes of the two lines are -3 and 3, respectively.
The product of the two slopes is -9, not -1, so the lines are neither parallel nor perpendicular.
61
Determine if the following two lines are parallel , perpendicular or neither:
Line 1: y = 2x + 3
Line 2: vertical line passing through the point (4, 5)
Vertical lines are considered to be parallel to each other, even though their slopes are undefined. Therefore, the two lines are parallel.
62
Angle
A figure formed by two rays with a common endpoint
- Angles are represented by three capital letters, with the vertex letter in the middle, such as ∠ABC.
63
Vertex
The common endpoint of an angle
64
Vertices
plural of vertex
65
We can name an angle by it's __________________
1. Vertex 2. By a point on each ray and the vertex 3. by an number
66
Acute angle
an angle that measures less than 90 degrees
67
Right angle
an angle that measures 90 degrees
68
Obtuse angle
An angle that measures more than 90 degrees but less than 180 degrees
69
Straight Angle
an angle that measures exactly 180 degrees
- Made from 2 opposite rays
70
Which of the following is a right angle?
A. 30°
B. 90°
C. 120°
D. 180°
B
71
Which of the following is an acute angle?
A. 30°
B. 90°
C. 120°
D. 180°
A
72
Which of the following is a straight angle?
A. 30°
B. 90°
C. 120°
D. 180°
D
73
Which of the following is an obtuse angle?
A. 30°
B. 90°
C. 120°
D. 180°
C
74
Transversal
a line that intersects two or more lines
75
Adjacent angles
Two angles that share a common side and have the same vertex
76
Non-adjacent angles
Two angles that do not have a common side or a common vertex (not touching)
77
Vertical Angles
A pair of opposite congruent angles formed by intersecting lines
78
Supplementary angles
2 angles whose sum is 180 degrees
- The angles formed by a straight line
- The angles formed by two opposite sides of a rectangle
- The angles formed by two alternate interior angles when a transversal intersects two parallel lines
79
Complementary angles
two angles whose measures have a sum of 90 degrees
-When two angles add to 90°, we say they "Complement" each other.
- Complementary comes from Latin completum meaning "completed" because the right angle is thought of as being a complete angle.
80
Corresponding angles
Angles in the same place on different lines they are equal in size.
81
Exterior angle
the angle between any side of a shape, and a line extended from the next side
- The angle formed from the extended side and the side that was next to (i.e. adjacent to) the original side . This angle will always be less than 180 degrees
82
Interior Angle
An angle formed by two sides of a polygon with a common vertex
- an angle that is inside the polygon
83
Alternate interior angles
Interior angles that lie on opposite sides of the transversal
84
Alternate exterior angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
85
When we add up the Interior Angle and Exterior Angle we get a _________________ so they are ___________________
Straight Angle, Supplementary Angles
86
An angle inside a shape
Interior Angle
87
The angle between any side of a shape, and a line extended from the next side.
Exterior Angle
88
If ∠E=45∘, what is the measure of ∠F if ∠E and ∠F are corresponding angles?
45 degrees
89
Which of the following is NOT a corresponding angle pair?
(A) ∠2 and ∠7
(B) ∠3 and ∠6
(C) ∠1 and ∠5
(D) ∠4 and ∠5
A
90
What is the definition of supplementary angles?
2 angles whose measures add up to 180º
91
If ∠G=60∘ and ∠G and ∠H are corresponding angles, what is the measure of ∠H?
60 degrees
92
If angle A is complementary to angle B, and the measure of angle B is 60°, what is the measure of angle A?
(A) 30°
(B) 45°
(C) 60°
(D) 90°
A
93
What is the definition of complementary angles?
2 angles whose measures add up to 90º
94
If ∠A=60∘, what is the measure of ∠B if ∠A and ∠B are supplementary?
120 degrees
95
Which of the following is a vertical angle pair?
(A) ∠1 and ∠6
(B) ∠2 and ∠5
(C) ∠3 and ∠4
(D) ∠4 and ∠6
C
96
What is the definition of corresponding angles?
Angles that are in the same position relative to a transversal intersecting two parallel lines.
97
Quadrilateral
a polygon with four sides and four angles
- a closed figure with four sides that are line segments
- has 4 vertices
- It is a 2D shape
98
Which of the following is a pair of alternate interior angles?
(A) ∠1 and ∠5
(B) ∠2 and ∠6
(C) ∠4 and ∠7
(D) ∠3 and ∠6
D
99
What is the sum of the interior angles of any quadrilateral?
360°
100
Square
A flat shape with 4 sides where:
* all 4 sides have equal length
* every interior angle is a right angle (90°)
* It is a kind of rectangle
* It is a Quadrilateral
101
Parallelogram
A flat shape with 4 sides where:
* Opposite sides are parallel
* Opposite sides are equal in length
* Opposite angles are equal
102
Rhombus
A quadrilateral with four equal sides
* All sides have equal length
103
Rectangle
A parallelogram with four right angles (90°)
* Opposite sides (sides across from each other ) are the same length and they are parallel
104
Trapezoid
A quadrilateral with exactly one pair of parallel sides
There is no defined measure for the angles or the lengths of the sides
105
A supplementary angle to a 30° angle is a:
A. 60° angle
B. 90° angle
C. 120° angle
D. 150° angle
B
106
A quadrilateral has angles measuring 60∘, 90∘, and 120∘. What is the measure of the fourth angle?
90
107
A quadrilateral has angles measuring x, y, z, and w. What is the measure of angle x if y = 100°, z = 110°, and w = 120°?
A. 30°
B. 40°
C. 50°
D. 60°
A
108
What are the properties of a rhombus?
Four congruent sides, four angles of equal measure
109
A quadrilateral has two opposite angles measuring 135° each. What is the measure of one of the other two angles?
A. 45°
B. 90°
C. 135°
D. 180°
A
110
What are the properties of a square?
Four right angles, four congruent sides
111
A quadrilateral has angles measuring x, y, z, and w. What is the equation that expresses the relationship between the four angles?
A. x + y + z + w = 180°
B. x + y + z + w = 360°
C. x + y + z + w = 540°
D. x + y + z + w = 720°
B
112
What are the properties of a trapezoid?
Exactly one pair of parallel sides, one pair of non-parallel sides
113
Which of the following quadrilaterals has opposite sides that are parallel and congruent?
A. Square
B. Rectangle
C. Rhombus
D. Trapezoid
B
114
Which of the following quadrilaterals has four right angles?
A. Square
B. Rectangle
C. Rhombus
D. Trapezoid
A
115
A rectangle has four right angles.
What is the sum of the measures of all its angles?
90
116
List the name of 4 sided plane figures that exhibit the following properties ; Four right angles
Rectangle, Square
117
List the name of 4 sided plane figures that exhibit the following properties ; Opposite sides are equal in length
Parallelogram, Rectangle, Square, Rhombus
118
List the name of 4 sided plane figures that exhibit the following properties ; Exactly one pair of parallel sides
Trapezoid
119
List the name of 4 sided plane figures that exhibit the following properties ;
All angles are equal in measure
Rectangle, Square
120
List the name of 4 sided plane figures that exhibit the following properties ;
Opposite angles are equal in measure
Rectangle, Square, Rhombus, Parallelogram
121
List the name of 4 sided plane figures that exhibit the following properties ;
All 4 sides are equal in length
Square, Rhombus
122
List the name of 4 sided plane figures that exhibit the following properties ;
Sum of interior angles is 360 degrees
Rectangle, Square, Rhombus, Parallelogram, Trapezoid : All four sided figures
123
List the name of 4 sided plane figures that exhibit the following properties ;
4 equal angles and 4 equal sides
Square
124
Triangle
A polygon with three sides.
125
Equilateral triangle
a triangle with 3 congruent sides and angles
126
Isosceles Triangle
a triangle with at least two congruent sides
127
Scalene triangle
a triangle with no congruent sides
128
Acute triangle
A triangle with 3 acute angles
129
Right triangle
A triangle that has a 90 degree angle.
130
Obtuse triangle
A triangle with one angle that is greater than 90 degrees.
131
Oblique Triangle
a triangle that is not a right triangle
132
Equidistant
The same distance (from each other, or in relation to other things).
Example: parallel lines are always equidistant
133
Median of a triangle
A line segment from a vertex (corner point) to the midpoint of the opposite side.
- Has equal line segments
134
Altitude of a triangle
a perpendicular line segment drawn from a vertex of a triangle to the opposite side
- Doesn't necessarily split the opposite side into equal segments.
-Isn't always inside a triangle.
135
Perpendicular bisector of a triangle
a segment that passes through the midpoint of a side and is perpendicular to that side.
- Does not have to start at vertex
- a line that passes through the midpoint of the side
136
Angle Bisector of a triangle
a line segment that bisects one of the vertex angles of a triangle
- it cuts the vertex angle in half
137
At equal distances
equidistant
138
A segment that divides an angle of a triangle into two congruent angles.
Angle bisector
139
True or False : The medians of a triangle always intersect inside the triangle
True
140
True or false: The altitudes of a triangle always intersect inside the triangle.
False
141
True or false: The angle bisectors of a triangle always intersect inside the triangle.
True
142
What is the perpendicular bisector of a side of a triangle?
A. A line that passes through the midpoint of the side and is perpendicular to it.
B. A line that passes through the vertex of the triangle and is perpendicular to the opposite side.
C. A line that passes through the midpoint of the side and is parallel to the opposite side.
D. A line that passes through the vertex of the triangle and is parallel to the opposite side.
A
143
What is the ratio of the segments created by an angle bisector on a side of a triangle?
A. The ratio of the measures of the two exterior angles that the bisector creates.
B. The ratio of the lengths of the other two sides of the triangle.
C. The ratio of the measures of the two angles that the bisector divides.
D. The ratio of the lengths of the other two angles of the triangle.
C
144
Concurrence (geometry)
The intersection of two or more lines, rays, or segments at a single point.
145
Concurrence (geometry in triangles)
The intersection of three or more lines, rays, or segments at a single point in a triangle.
146
Centroid
The point of concurrency of the medians of a triangle
- Point where 3 medians meet
- Always on the inside of triangle
-Segments are split in 2:1 ratio
147
Circumcenter
the point of concurrency of the three perpendicular bisectors of a triangle
- Point where 3 perpendicular bisectors meet
-Not always on inside of triangle
-Circumcenter is equidistant from angle
-Center of circumscribed circle
148
Orthocenter
The point of concurrency of the altitudes of a triangle
-Point where 3 altitudes meet
-Not always on inside of triangle
-It is the center of right angled lines in a triangle
-Ortho means " striaght" or " right"
149
What is the point of concurrency of the perpendicular bisectors of a triangle?
A. The incenter
B. The circumcenter
C. The orthocenter
term-178
D. The centroid
C
150
Which of the following points is equidistant from the vertices of a triangle? (Select all that apply)
A. Incenter
B. Circumcenter
C. Orthocenter
D. Centroid
A and B
151
What is the point of concurrency of the angle bisectors of a triangle?
A. The circumcenter
B. The incenter
C. The orthocenter
D. The centroid
B
152
Which of the following points are always inside a triangle?
A. Centroid
B. Circumcenter
C. Orthocenter
D. Incenter
E. None of the above
D
153
Which of the following points can be outside a triangle?
(Select all that apply)
A. Incenter
B. Circumcenter
C. Orthocenter
D. Centroid
B and C
154
Which of the following points are concurrent in a triangle?
A. Incenter and circumcenter
B. Circumcenter and orthocenter
C. Orthocenter and centroid
D. Centroid and incenter
E. All of the above
E
155
Which of the following points are always outside a triangle?
A. Incenter
B. Circumcenter
C. Orthocenter
D. Centroid
B
156
Area
The number of square units required to cover a surface.
- It is a two-dimensional measurement.
157
Perimeter
The sum of the lengths of the sides of a polygon
- the total length of all its sides added together.
- It is a one-dimensional measurement.
158
The area of a rectangle is
Area = Length x Width
159
The area of a triangle
Area = 1/2 base x height
160
How do you determine the perimeter of a rectangle?
Step 1 : add up the lengths of all four sides.
Step 2 : Since opposite sides of a rectangle are always equal, you can simply add up the length and the width, and then multiply this sum by two
161
Is the following an example of perimeter or area? :
the amount of space that the pool takes up.
Area
162
How do you determine the perimeter of a triangle?
Add up the lengths of all the sides.
163
Is the following an example of perimeter or area? :
The measure of the length of the outline of a shape
Perimeter
164
Is the following an example of perimeter or area? :
the total length of the fence.
Perimeter
165
Is the following an example of perimeter or area? :
The measure of the amount of space inside the shape.
Area
166
Is the following an example of perimeter or area? :
The amount of water needed to fill a swimming pool
Area
167
Is the following an example of perimeter or area? :
the total length of the edges of the rug.
Perimeter
168
Is the following an example of perimeter or area? :
The amount of paint needed to paint a wall
Area
169
Is the following an example of perimeter or area? :
The length of a running track
Perimeter
170
Is the following an example of perimeter or area? :
The amount of ribbon needed to wrap around a gift box
Perimeter
171
A rectangle has a length of 10 cm and a width of 5 cm. What is its perimeter?
30 cm
172
A rectangular garden has a perimeter of 40 m.
If the length of the garden is 12 m, what is its width?
14 m
173
A rectangular field has a length of 150 m and a width of 100 m.
How many meters of fencing are needed to fence the field?
500 m
174
A triangle has sides of length 3 cm, 4 cm, and 5 cm. What is its perimeter?
12 cm
175
An equilateral triangle has sides of equal length.
If the perimeter of the triangle is 18 cm, what is the length of each side?
6 cm
176
Pythagorean theorem
A mathematical formula that states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
177
Pythagorean Theorem Formula
a² + b² = c²
178
Hypotenuse
The longest side of a right triangle, opposite the right angle.
179
Legs
The two shorter sides of a right triangle, adjacent to the right angle.
180
Pythagorean Triple
A set of nonzero whole numbers that satisfy the Pythagorean Theorem
181
A right triangle has legs of length 3 cm and 4 cm. What is the length of the hypotenuse?
5 cm
182
A ladder is leaning against a wall, forming a right triangle. The base of the ladder is 4 feet from the wall, and the top of the ladder is 10 feet high. How long is the ladder?
10.8 feet
183
Which of the following is NOT a Pythagorean Triple?
A. 3, 4, 5
B. 5, 12, 13
C. 7, 24, 25
D. 9, 40, 41
C
184
A right triangle has a hypotenuse of 10 cm and a leg of 6 cm. What is the length of the other leg?
A. 4 cm
B. 8 cm
C. 10 cm
D. 12 cm
B
185
A rectangle has a length of 8 cm and a width of 6 cm. What is the length of the diagonal of the rectangle?
A 10 cm
B 12 cm
C 14 cm
D 16 cm
D
