2016Chapter 7 GeometryFST
7-3 Triangle Similarity: AA, SSS, and SAS
HW:2,4,8,10,13-23 odd,30,34,35
Triangle Congruence / vs / Triangle SimilarityExample 1:
Explain why the triangles are similar and write a similarity statement.
List the similarity statements for each of the sides:
Example 2:
Verify that the ∆PQR and ∆STU triangles are similar.
Example 3:
Verify that the triangles ∆DEF and ∆HJK are similar.
Example 4:
Explain why ∆ABE ~ ∆ACD, and then find CD.
Example 5:
The photo shows a gable roof. AC || FG. ∆ABC ~ ∆FBG. Find BA to the nearest tenth of a foot.
7-4: Applying Properties of Similar Triangles
HW: 3-21 every third problem, 22,26-34 even
Artists use mathematical techniques and ratios to make two-dimensional paintings and drawings appear three-dimensional. This is called adding perspective. Far away objects can be made to look smaller, and close up objects look bigger without distorting them.
Example 1:
Find US.
Example 2:
Verify that DE || BC.
Example 3:
Suppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch.
Which gets us to…
Example 4:
Find PS and SR.
7-6: Dilations and Similarity in the Coordinate Plane
HW: 10-18 even, 21-35
A ______is a transformation that changes the size of a figure but not its shape.
The ______and the image are always similar.
A ______describes how much the figure is enlarged or reduced.
For a dilation with scale factor k, you can find the image of a point by multiplying each coordinate by k: (a, b) (ka, kb).
Hint:
If the scale factor of a dilation is greater than 1 (k > 1), it is an ______. If the scale factor is less than 1 (k < 1), it is a______.
Example 1:
Draw the border of the photo after a dilation with scale factor 5/2.
Example 2:
Given that ∆TUO ~ ∆RSO, find the coordinates of U and the scale factor.
Example 3:
Given: E(–2, –6), F(–3, –2), G(2, –2), H(–4, 2), and J(6, 2).
Prove: ∆EHJ ~ ∆EFG.
Example 4:
Graph the image of ∆ABC after a dilation with scale factor 2/3.
Verify that ∆A'B'C' ~ ∆ABC.
11-7: Circles in the Coordinate Plane
HW: 10-14, 19-20, 46
The equation of a circle is based on the Distance Formula and the fact that all points on a circle are equidistant from the center.
Equation of a circle with radius r:
Example 1: Write the equation of each circle.
J with center J (2, 2) and radius 4 / K that passes through J(6, 4) and has center K(1, –8)Example 2:
Graph x2 + y2 = 16.
x / yExample 3:
Graph (x – 3)2 + (y + 4)2 = 9.
Example 4:
A carpenter is planning to build a circular gazebo that requires the center of the structure to be equidistant from three support columns located at E(–2, –4), F(–2, 6), and G(10, 2).
What are the coordinates for the location of the center of the gazebo?