Tear off a small piece of paper and answer the question below. When you are done place the paper in the basket and then take out your homework, notebook,

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Presentation transcript:

Tear off a small piece of paper and answer the question below. When you are done place the paper in the basket and then take out your homework, notebook, and pen/pencil. Bump in the Road Write down something you found confusing from material covered yesterday.

Properties of Dilations Module 3 LP2

Example 1: Dilating a segment Dilate with a scale factor =2 from. O is a point off of segment PQ.

Draw rays from point through each of the points and.

Using a compass, measure the distance from O to P.

Repeat the process to locate Q’.

Connect points ′ and ′ to draw line segment P′Q’.

Hmmmmmm Notice the dilation produced a line segment and that line segment is parallel to the original. What would happen if we selected a different location (point E for example) for the center or different points P and Q? The dilation would still produce a segment and that segment would be parallel to the original.

Hmmmmmm

Example 2 With a scale factor =3, Is the dilated segment, P′Q’, still parallel to segment PQ? Yes…think about the angles created by the transversals.

Example 3 What if we moved center O to the line?

What we have shown: a line segment, after a dilation, is still a line segment. Mathematicians like to say that dilations map line segments to line segments.

Example 4: Working with Scale Factor

Step 1: Use a ruler to measure the length of OA and OB. 7

Step 2: Calculate

Step 3: Mark off the points on their respective rays and connect ′ to ′

Question What happened to our segment AB after the dilation? When we connect point ′ to point ′, we will have segment A’B’ which is parallel to the segment AB.

And what do we know about parallel lines or parallel line segments? 7 3.5

And what do we know about parallel lines or parallel line segments? c o r r e s p o n d i n g a n g l e s ! c o r r e s p o n d i n g a n g l e s ! 7 3.5

Properties of Dilations  Dilations map segments to segments, with a certain scale factor (r).  Dilations map angles to angles which have the same degree

Observations  The length of the dilated line segment is the length of the original segment, multiplied by the scale factor.  The measure of an angle remains unchanged after a dilation.