Definitions
AA Similarity Statement
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar
Pre-image : (2,2) Image: (5,5) What is the scale factor?
2.5 or 5/2
The value of z in: z/4 = 15/12
z=5
One triangle has angles measuring 30, 60, 90 and the second triangle has angles measuring 30, 60, 90. Are the triangles similar? Why?
yes. AA
Any two points on a line should have _______ slope.
Same
Similar
two figures of the same shape but not necessarily the same size
Pre-image: (28,83) Image: (140, 415) What is the scale factor?
5
Two corresponding sides of similar triangles have the lengths of 24 cm and 60 cm. What would be the ratio of the side lengths?
2/5
Two line segments, AB and CD intersect at point E to form Triangles AEC and BED. Line segments AC and BD are parallel. Is triangle AEC similar to triangle BED?
Yes by AA
Find the slope of the line that passes between the pair of points.
(1, 1) and (7, 5)
4/6 or 2/3
Scale Factor
The ratio of any two corresponding lengths of the sides of two similar figures.
Pre-image: (46,37) Scale factor: 1/2 What is the Image?
(23,18.5)
Two triangular roofs are similar. The corresponding sides of these roofs are 16 feet and 24 feet. If the altitude of the smaller roof is 6 feet, find the corresponding altitude of the larger roof.
9 feet
Triangle ABC has side lengths 12, 16, and 20 and Triangle DEF has side lengths 36, 64, 100. Are the triangles similar? Why or why not?
No. Sides are not proportional
(2, 5) and (-1,2)
7/3
Proportional
Having a constant ratio to another quantity
Pre-Image: (222,17) Scale Factor: 34 What is the Image?
(7548,578)
Triangle ABC is similar to Triangle DEC. BC is 15 units long, EC is 6 units long, and DC is 5 units long. What is the length of AD.
7.5
Side AB of Triangle ABC has a side length of X+1 and Side AC has a side length of X+5. Side HG of Triangle HGJ has side length of 3 and Side HJ has side length 6. Angles BAC and GHJ are congruent and Angles ACB and HJG are congruent. Are the triangles similar? If so solve for x. If not, explain why.
yes they are similar. X=3
Given two points (4,5) and (8,10) are on the same line, would (16,20) also be a point on the line? Explain how you know.
Also the triangle would be similar if drawn on graph paper - the sides are proportional (rise/run) is the same value when simplified.
Rigid Motion
A transformation done to a figure that maintains the figure's shape and size or its segment lengths and angle measures.
Scale Factor: 3 Image: (161.1, 107.4) What is the Pre-image?
(53.7, 35.8)
A flag pole casts a shadow of 15.5'. A 3' stick casts a shadow of 4' at the same time of day. What is the height of the flagpole?
x=11.625 ft
Use similar triangles to solve: A tree casts a shadow that is 24 feet long. A person who is 5 feet tall is standing in front of the tree, and his shadow is 8 feet long. Approximately how tall is the tree?
15 ft
Select all of the points that are on the line through (0,5) and (2,8)
A. (5,10)
B. (6, 14)
C. (30, 50)
D. (40, 60)
B. (6, 14)
C. (30, 50)
Using the coordinate and one that is given on the line - they have the same slope as the pair in the directions of 3/2.