Module 4 ­ Lesson 5 ­ Converse of the FTS
Friday. November. 20. 2015.
Students know the converse of the fundamental theorem of similarity and students use the FTS to find the location of dilated points on the plane.
Have homework out.
1
Module 4 ­ Lesson 5 ­ Converse of the FTS
The Fundamental Theorem of Similarity ­ States that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle’s third side.
2
Module 4 ­ Lesson 5 ­ Converse of the FTS
Going back to our objective..
Students know the converse of the fundamental theorem of similarity ...
What does "converse" mean?
3
Module 4 ­ Lesson 5 ­ Converse of the FTS
To form the converse of a statement, interchange the hypothesis and the conclusion. Statement: If A, then B. Converse: If B, then A.
Statement:"If it is raining outside, the ground is wet." Converse: "If the ground is wet, it is raining outside"
Statement: If a quadrilateral is a rectangle, then it has two pairs of parallel sides.
Converse: If a quadrilateral has two pairs of parallel sides, then it is a rectangle.
4
Module 4 ­ Lesson 5 ­ Converse of the FTS
The FTS
If: We have a dilation.
The Converse of FTS
If: PQ || P'Q' and |P'Q'| = r|PQ|
Then: PQ || P'Q' and Then: We have a dilation.
|P'Q'| = r|PQ|
If: There is a dilation
Then: The line segment and the dilated line segment are parallel and the length of the line segment multiplied by the scale factor is equal to the length of the dilated line segment
If: If we have two segments that are parallel to one another and the length of the segment times the scale factor equals the length of the dilated segment.
Then: We have a dilation.
5
Module 4 ­ Lesson 5 ­ Converse of the FTS
Open your Eureka Books to page S.21
6
Module 4 ­ Lesson 5 ­ Converse of the FTS
Exercise 1
a. Determine the scale factor r.
7
Module 4 ­ Lesson 5 ­ Converse of the FTS
Exercise 1
b. Locate the center O of dilation. Measure the segments to verify that |OP'| = r|OP| and |OQ'| = r|OQ|. 8
Module 4 ­ Lesson 5 ­ Converse of the FTS
In the diagram, we have center O and ray OA . We want to find the coordinates of point A' . We are given that the scale factor of dilation is r = 2
9
Module 4 ­ Lesson 5 ­ Converse of the FTS
Complete Exercise 2 in Your Eureka Books on Page S.22
10
Module 4 ­ Lesson 5 ­ Converse of the FTS
Exercise 2. What you should have.
11
Module 4 ­ Lesson 5 ­ Converse of the FTS
12
Module 4 ­ Lesson 5 ­ Converse of the FTS
13
Module 4 ­ Lesson 5 ­ Converse of the FTS
14