Math 2 Unit 6 Review (similarity)
Two figures are said to be similar if:
(1) Their corresponding angles are congruent AND (2) Their corresponding sides are in proportion
Dilation
A transformation that changes the size of an object, but not the shape.
the student was correct
After a dilation with a center of (0, 0), a point was mapped as (1, 4) → (4, y). A student determined y to be 16. Evaluate the student's answer.
the student incorrectly divided by the scale factor instead of multiplying it
After a dilation with a center of (0, 0), a point was mapped as (4, -6) → (12, y). A student determined y to be -2. Evaluate the student's answer.
Triangle Angle Bisector Theorem
An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Definition of similar polygons
Corresponding <s are congruent and the lengths of corresponding sides are proportional
Similar
Figures that have the same shape but not necessarily the same size
< D
Fill in the missing information
< Q
Fill in the missing information
< R
Fill in the missing information
Segment DF
Fill in the missing information
Segment ED
Fill in the missing information
Segment FE
Fill in the missing information
20m
How tall is the tree?
AA~
If 2 <s of one 🔺 are congruent to 2 <s of another 🔺, then the 2 🔺 are ~.
Scale factor
If 2 polygons are ~, then the ratio of the lengths of 2 corresponding sides is called the _______________.
Side-Splitter Theorem
If a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.
SAS~
If the lengths of the 2 corresponding sides of 2 🔺 are proportional and the included <s are congruent, then the 🔺 are ~.
SSS~
If the lengths of the corresponding sides of two 🔺 are proportional, then the 🔺 are ~.
Enlargement
If the scale factor is 2.2, is the dilation an enlargement or a reduction?
AA similarity
If two angles of one triangle are congruent to two angles of another triangle, then the the triangles are similar
smaller than
In a dilation with a scale factor of 3/4, the new image is __________ the original image.
Center of Dilation
In a dilation, the fixed point about which the figure is enlarged or reduced
24
Solve for DE
8
Solve for PQ
14
Solve for PR
20
Solve for the missing side
6
Solve for u
12
Solve for x
17.5
Solve for x
2
Solve for x
Proportional
The relationship of one thing to another in size, amount, etc.
1
Under a dilation centered at the origin, the new image is congruent to the original image. What is the scale factor?
(-1,2)
What are the coordinates of the new image of the point (-3, 6) after a dilation with a center of (0, 0) and scale factor of 1/3?
(8, -16)
What are the coordinates of the new image of the point (2, -4) after a dilation with a center of (0, 0) and scale factor of 4?
1.5
What is the scale factor if Triangle A is the original figure?
2/3
What is the scale factor if Triangle B is the original figure?
1/2
What is the scale factor of the smaller figure to the larger figure?
Multiply coordinate by scale factor
When given an (x,y) coordinate and scale factor, how is the prime coordinate calculated?
Corollary to Side-Splitter Theorem
When three parallel lines intersect two transversals, then the segments intercepted on the transversal are proportional.
Scale Factor
the ratio of the lengths of two corresponding sides
