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Transcript of Tear off a small piece of paper and answer the question below. When you are done place the paper in...
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 foundconfusing from material covered yesterday.
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
How would the work we did change if the scale factor were instead of ?We would have to find a point ′ so that it is 𝑃3 times the length of , instead of twice 𝑂𝑃the length of 𝑂𝑃. Same for the point ′𝑄 .(Repeat the compass steps again.)
Example 2
With a scale factor =3, 𝑟Is the dilated segment, P′Q’, still parallel to segment PQ?
Yes…think about the angles created by the transversals.
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
Given center O off segment AB with rays drawn from center O, through points and …𝐴 𝐵Dilate the segments OA and OB with a scale factor
Question
What happened to our segment AB after the dilation?When we connect point 𝐴′ to point 𝐵′, 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?
corre
spondi
ng angles!
correspondi
ng angles!
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