Transcript BPW 1.4 Properties of Transformations.pptx

Math CC7/8 – Be Prepared
On Desk:
Learning Log:
1. Pencil
2. Protractor
3. Math Journal
4. BPW Learning Log
1. HW: p. 23 #19-24, #39 (WS #39 only)
Polyptych – due Wed. 5/18?
2. Turn in TwMM books!
3. Parent Signatures-Test/LL?!
Tasks for Today
• Lesson 1.4 – Properties of Transformations
Notes
When making transformations of figures, you
need to pay attention to two important things:
Angle
Distance
_______________
and _______________
.
Reflection:
• Maintain a 90 degree angle with perpendicular bisector
• Original point and image must be SAME distance from line of reflection
Rotation:
• Mark CENTER of rotation
• Rotate each point the same angle
• Measure distance of each point from center of rotation
Translation:
• Keep parallel lines of slide
• Measure distance of slide
Center of
Rotation = O
Center of
Rotation = O
The distances between the vertices in
the original figure are equal to the
distances between the corresponding
vertices in the image.
The angle measures of the original are equal to the corresponding
angles measures on the image. And XOX’ and YOY’ are the same
under the rotation about the center O.
Center of
Rotation = O
Any line segment that is parallel in the original figure is
also parallel in the image figure. Segments that join an
original point to the corresponding image point are
parallel to each other under translation
Center of
Rotation = O
It seems as though all points/or lines are “unmoved”…
But if you think about the whole plane being moved–
• the points on the line of reflection are unmoved
• the center of rotation stays unmoved
• But in a translation – all points, segments and lines are
moved
Center of
Rotation = O
Properties that are preserved – or stay the same:
• Length of segments
• Measures of angles
• Any parallel relationships
• Area and perimeter of each figure
• Translation retains orientation of the figure