Angle and Line Relationships
Two angles that add up to 90 degrees are called
Complementary Angles
The sum of all interior angles of a triangle is
180 degrees
Determine 3 ways to define a polygon.
-2D (flat)
-enclosed
-straight edges/lines
Name and define the 4 transformations
Translation - slide
Reflection - flip
Rotation - turn
Dilation - enlarge/reduce
What math property is represented below?
x + 4 = 4 + x
Commutative Property of Addition
If m<d and m<e are both supplementary angles, and m<d is 45 degrees. What is the value of m<e?
m<e: 135 degrees
(supplementary angles = 180 degrees)
Triangles can be classified with their angles and sides. What are all the ways a triangle can be classified due to its angle(s)?
-Acute (all acute angles, less than 90 degrees)
-Obtuse (an angle more than 90, less than 180 degrees)
-Right (one 90 degree angle)
Find the sum of the measures of the interior angles of a heptagon.
900 degrees
Suppose triangle ABC is translated 2 units right and 1 units down. Find the coordinates of the vertices of its image.
A (4, 1) B: (2, 3) C (0, 1)
A' (6, 0) B' (4, 2) C' (2, 0)
Define absolute value and provide an example.
Definition: The distance a number is from zero.
Examples Will Vary: | -3 | = 3
*Absolute value CANNOT be negative*
Corresponding angles and alternate angles create congruent angles. What letter do they each create to represent these congruent angles?
-Corresponding angles create an "F" shape
-Alternate angles create a "Z" shape
Find the value of x in triangle ABC if m<A is 89 degrees, m<B is 48 degrees, and m<C is x.
m<C = 43 degrees
The surface of a soccer ball contains 12 regular pentagons and 20 regular hexagons. What is the measure of one interior angle of a pentagon?
108 degrees
The vertices of figure DEFG are D(3, –1), E(4, –4), F(1, –3), and G(0, 0). What are the coordinates of the vertices of the image after a reflection over the y-axis?
D'(–3, –1) E'(–4, –4) F'(–1, –3) G'(0, 0)
Solve and provide answer in lowest term.
2/3 x 3/6
1/3
Angles ABC and CBD are adjacent angles that have a total measure of 152 degrees. Find the value of each angle if angle ABC is 6x and angle CBD is 2x.
-Angle ABC = 114 degrees
-Angle CBD = 38 degrees
Classify triangle DEF that has angle values 68, 68, 44 degrees.
Acute Isosceles Triangle
What is the measure of one interior angle of an 18-gon?
160 degrees
If you have a figure in quadrant I and you are asked to rotate it 270 degrees counterclockwise, where is the figure located at now and what is its ordered pair?
quadrant IV - (x, -y)
Write the following in scientific notation.
0.0679
6.79 x 10-2
Angles DEF and EFG are vertical angles. Find the value of x if angle DEF is 12x + 10 and angle EFG is 5x + 31.
x = 3
In triangle XYZ, its angles are characterized as m<X (3x), m<Y (4x + 12), and m<Z (x). Find the value of each angle.
m<X (3x) = 63 degrees
m<Y (4x + 12) = 96 degrees
m<Z (x) = 21 degrees
Determine whether or not a tessellation can be created using only regular octagons. If not, explain.
No; each interior angle of a regular octagon measures 135° and 360° is not evenly divisible by 135°.
Starting vertices: A (0.5, -4), B (3, 1), C (−2, 1)
Ending vertices: A′(0.5, 4), B′(3, −1), C′(−2, −1)
What transformation has been made and over what axis?
Reflection over the x-axis
Define a natural number, whole number, integer, rational number, and irrational number.
natural number: 1, 2, 3... (positive whole)
whole number: 0, 1, 2... (includes 0, positive whole)
integer: -2, -1, 0, 1, 2... (includes 0, positive/negative whole)
rational number: -1, 0, 1, 0.75, 1/3 (all numbers, excluding irrational numbers)
irrational number: π - pie (cannot be made into a ratio, weird #)