Dilation
What do you call the number that represents the ratio between two similar figures?
Scale Factor
True or False: Similar Figures can be obtained ONLY by performing a dilation from one to the other.
False. Similar figures can also be obtained through a dilation and additional rigid motions, such as a reflection, translation, or rotation.
True or False: All equilateral triangles are similar.
True.
(x/10) = (2/5). What is the value of x?
x=4
The ratio of a length on an image to the corresponding length on the preimage
Scale Factor
What do we call a dilation in which the figure gets bigger?
Enlargement
All angles must be _______ to the corresponding angle for two figures to be similar
Triangle 1 and Triangle 2 are similar. Triangle 1 has angles of 50 degrees and 75 degrees. What are the angles of triangle 2?
50 degrees, 75 degrees, and 55 degrees.
(x+1)/2 = 3/4
Find the value of x.
x=2
The point from which dilations are performed
Center of dilation
What do we call a dilation in which the figure gets smaller?
Reduction
In similar triangles, all corresponding side lengths are ___________
proportional
What are the three sufficient side and angle relationships that are enough to know that two triangles are similar?
Angle-Angle, Side-Angle-Side, Side-Side-Side
(x-3)/(2x-1) = 1/7
Find the value of x.
x=4
A segment that connects the midpoints of two sides of a triangle.
Midsegment
Find the scale factor needed to take a triangle with hypotenuse 6 and turn it into a triangle with hypotenuse of 3.
.5 or 1/2
Polygon 1 and Polygon 2 are similar. The perimeter of Polygon 1 is 25 cm and each side length of the polygon is 5cm long. The scale factor between Polygon 1 and Polygon 2 is k=4. What is the perimeter of Polygon 2?
100cm
Which Angle and Side relationship that we discussed in class is not sufficient for us to know that two figures are similar?
Angle-Side-Side
Triangle ABC ~ Triangle DEF.
AB = 6, DE = 12 and EF = 10. Find the length of BC.
BC = 5
A line that intersects two or more parallel lines.
Transversal
A figure with vertices at P- (2, 4), Q- (-1, 3), R- (3,-2), and S- (-4,4) is dilated so that it now has vertices at P'- (3,6), Q'- (-1.5, 4.5), R'- (4.5,-3). Find the coordinates of the final vertex, S', after the figure has been dilated
(-6,6)
Mia has two rectangles. One has a length of 7 and a width of 5. The other has a length of 9 and a width of 7. Are these rectangles similar?
No. The side lengths are not proportional
Triangle ABC has side lengths AB = 4, BC = 6 and AC = 3. Triangle DEF has side lengths DE = 6, EF = 12, and DF = 8. Write a similarity statement between the two triangles.
ABC~DFE
An angle bisector splits the opposite side of a triangle into lengths of 6 and 9. If the one of the other sides of the triangle is 12, what are the other two possible side lengths of the triangle.
8 and 18
A pair of congruent angles formed when two lines intersect each other.
Vertical Angles