How Do Dilations Map Angles?
Related Topics:
Lesson Plans and Worksheets for Geometry
Lesson Plans and Worksheets for all Grades
More Lessons for Geometry
Common Core For Geometry
New York State Common Core Math Geometry, Module 2, Lesson 9
Student Outcomes
- Students prove that dilations map an angle to an angle with equal measure.
- Students understand how dilations map triangles, squares, rectangles, trapezoids, and regular polygons.
How Do Dilations Map Angles?
Classwork
Exploratory Challenge/Exercises 1β4
- How do dilations map triangles?
a. Make a conjecture.
b. Verify your conjecture by experimenting with diagrams and directly measuring angles and lengths of segments. - How do dilations map rectangles?
a. Make a conjecture.
b. Verify your conjecture by experimenting with diagrams and directly measuring angles and lengths of segments.
- How do dilations map squares?
a. Make a conjecture.
b. Verify your conjecture by experimenting with diagrams and directly measuring angles and lengths of segments. - How do dilations map regular polygons?
a. Make a conjecture.
b. Verify your conjecture by experimenting with diagrams and directly measuring angles and lengths of segments
Exercises 5β6
- Recall what you learned about parallel lines cut by a transversal, specifically about the angles that are formed.
- A dilation from center π by scale factor π maps β π΅π΄πΆ to β π΅β²π΄β²πΆβ². Show that πβ π΅π΄πΆ = πβ π΅β²π΄β²πΆβ².
Discussion
The dilation theorem for angles is as follows:
DILATION THEOREM: A dilation from center π and scale factor π maps an angle to an angle of equal measure. We have shown this when the angle and its image intersect at a single point, and that point of intersection is not the vertex of the angle.
Lesson Summary
- Dilations map angles to angles of equal measure.
- Dilations map polygonal figures to polygonal figures whose angles are equal in measure to the corresponding angles of the original figure and whose side lengths are equal to the corresponding side lengths multiplied by the scale factor.
Check out our most popular games!
Fraction Concoction Game:
Master fractions in the lab: mix, add, and subtract beakers to create the perfect concoction!
Fact Family Game:
Complete fact families and master the link between addition & subtraction and multiplication & division.
Number Bond Garden:
Clear the board by matching number pairs that sum to ten in this garden-themed mental math puzzle.
Online Addition Subtraction Game:
Practice your addition and subtraction skills to help the penguin find its mummy.
Penguin Solitaire:
Move all cards to the foundations to build four full sequences. There are two versions here: Penguin (Tuxedo) and Penguin (Original).
Sawayama Solitaire:
This is similar to the common Klondike Solitaire except for a few changes to make it more strategic.
Check out more Solitaire games here.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.