Transformations
What is a transformation that slides a figure without changing its shape or size called?
Translation
Solve and explain how many solutions there are:
4(x+3) = 4x + 8
4(x+3) = 4x + 8
4x + 12 = 4x + 8
12 = 8
No Solutions
What are the two angles called that are formed when two lines intersect? (See Ms. Pedersen)
Vertical Angles
What is the term for a line that crosses two or more other lines?
A transversal
Solve for x: 3(x - 2) = 12.
x=2
Describe what happens to a shape when it is reflected over the x-axis.
It's flipped over like a mirror
Solve for x:
x + 8 = 2(0.5x + 4)
x + 8 = 2(0.5x + 4)
x + 8 = x + 8
8 = 8
Infinite/Many Solutions
If two angles are complementary, what is the sum of their measures?
90 degrees
Name the angles that are formed on opposite sides of the transversal and inside the parallel lines. (see Ms. Pedersen)
Alternate interior angles
A rectangle has a length of 10 cm and a width that is 3 cm less than its length. What is the perimeter?
10 + 10 + 7 + 7 = 34 cm
What is the result of rotating a point (3, 2) 90 degrees counterclockwise around the origin?
(x, y) ---> (-y, -x)
Solve for x: 3(x-2) + 6 = 5(x+4)
3(x-2) + 6 = 5(x+4)
3x - 6 + 6 = 5x + 20
3x = 5x + 20
-2x = 10
x = -5
What is the relationship between the angles in an isosceles triangle?
two angles are equal/congruent
If two parallel lines are cut by a transversal, what can be said about the corresponding angles?
They are in the same location and are congruent/equal
If 5x + 3 = 2x + 15, what is the value of x?
x=4
If a triangle is dilated by a scale factor of 2, what happens to its area?
It's doubled/Multiplied by 2
Solve for n: 1.2n - 1.5 = 0.45n
1.2n - 1.5 = 0.45n
0.75n = 1.5
n = 2
If angle A measures 50 degrees, what is the measure of its supplementary angle?
180 - 50 = 130
What type of angle pairs are formed by a transversal intersecting two parallel lines?
corresponding angles, alternate interior angles, alternate exterior angles, and consecutive (same-side) interior angles
A triangle has angles measuring x, 2x, and 3x. What is the value of x?
x + 2x + 3x = 180
6x = 180
x = 30
If a shape is rotated 180 degrees clockwise around the origin, what happens to the shape?
It is completely flipped around/ on the opposite side of the graph.
Jordan buys two new jerseys and a glove for softball. She pays $44 for the glove and gives the clerk two fifty-dollar bills to pay the exact amount. How much does Jordan pay for each jersey?
2x + 44 = 50 + 50
2x + 44 = 100
2x = 56
x = 28
$28 per jersey
Describe the relationship between alternate interior angles when two parallel lines are cut by a transversal.
They are congruent/THE SAAAAAAAME
If angle 1 is 70 degrees, what is the measure of angle 2 if angle 1 and angle 2 are corresponding angles?
70 degrees
If a car travels at a speed of 60 mph for 2 hours and then at 45 mph for 3 hours, what is the total distance traveled?
(60 x 2) + (45 x 3)
120 + 135
255 Miles