Geometry Reflective Portfolio
Unit #6: Similarity
Complete this packet as your Study Portfolio#6!
Section #1: Vocabulary (words and/or diagrams)
· Similar figures -
· Dilation Transformation – include dilation notation
· Scale factor-
· Mid-segment of a triangle-
· Geometric mean-
Section #2: Formulas/Equations/Theorems (show work for examples)
1. Distance Formula:
Find the length of in simplest radical form, P (-3, 5) U(3, 7),
2. What 2 properties do similar triangles possess:
o Corresponding sides are______
o Corresponding angles are______
Example: Find the height of the flagpole to the nearest ft.
3. What are the three triangle similarity theorems? Describe each.
1)
2)
3)
4. Mid-segment Theorem ( 3 properties about a mid-segment):
a. ______
b. ______
c. ______
Example: M, N and O are midpoints of respectively, Find the perimeter of .
4. Triangle Proportionality Theorem (aka Side-Splitter Theorem): Write it out!
______
______
Example: Find the value of x. Non-example: Find the value of h.
Why is this a non-example of this theorem?
5. State the 2 right triangle similarity theorems. Then apply each theorem to the given example.
1) Altitude theorem-
______
2) Leg theorem-
______
Example: Find the altitude h.
Example: Find the length of leg AB in simplest radical form.
Section #3: Key methods and concepts :
Use the given examples to help you write out the process for each.
1. How do you find the perimeter of a figure in the coordinate plane?
Find the perimeter of in simplest radical form.
Step #1: Find the length of all 3 sides.
AB=
BC=
AC=
Step #2: Sum of all 3 sides P =______units
2. State the “shaded area or area of the box” process to finding the area of an irregular polygon in the coordinate plane as you find the area of LMNP.
3. How do you construct a dilation using a compass and straight edge?
Example: D1/2()
4. How do you find the center of dilation on and off the coordinate plane AND the scale factor?
Example: Coordinate plane Example: Non- coordinate plane
Example: Coordinate plane Example: Non- coordinate plane
Show how to find the scale factor Show how to find the scale factor
for the ex. above for the ex. above
5. What is the difference between a positive and negative scale factor?
6. How do you dilate a figure on the coordinate plane with the center at the origin?
Graph and state the coordinates of A’B’C’ after a dilation of scale factor ½.
7. How do you dilate a figure on the coordinate plane with the center that is not the origin?
8. How do you find the rule to dilate a figure on the coordinate plane with the center that is not the origin?
Write out the 3 step process using the given example and then dilate the O(-6, 9) by a scale factor of 2/3 and center of dilation at (3, 6).
1)
2)
3)
9. How do you dilate a line on the coordinate plane?
The line y = 5x – 6 is dilated by a scale factor of 3/2 and centered at the origin. What is the equation of the image of the line after the dilation?
Show the steps for this process:
10. Show how to find the missing side (value of x) of a pair of similar figures.
11. State the missing reasons.
AA similarity theorem.
______
______