Cogito
Geometry · Chapter 2 · Lesson 1
Rigid Motions and Symmetry
Moves that preserve everything but position.
10 problems · about 19 minutes · G-CO.A.2, G-CO.A.3, G-CO.A.5
What this lesson teaches
The student performs and composes rigid motions and identifies symmetry.
- Rigid motions preserve lengths and angles.
- Two parallel reflections make a translation.
- Symmetry is a transformation that maps a figure onto itself.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Angles in Polygons: Interior sum of a heptagon (7 sides), in degrees?
Answer 900
Why 900°.
Review — Angle Pairs and Parallel Lines: Co-interior with 125°, lines parallel. What is it?
Answer 55
Why 55°.
Warm Up
Straightforward practice. Get the method working first.
4 problemsA regular octagon maps onto itself after how many degrees, at minimum?
Answer 45
Why 45°.
Two reflections in parallel lines compose to what?
Answer A translation.
Why A translation.
Lines of symmetry in an equilateral triangle?
Answer 3
Why One through each vertex.
A regular pentagon maps onto itself after how many degrees, at minimum?
Answer 72
Why 360 ÷ 5.
Build It Up
The same ideas with more to keep track of.
2 problemsDo rigid motions change side lengths?
Answer No.
Why That is what rigid means.
Lines of symmetry in a rectangle that is not a square?
Answer 2
Why Not the diagonals.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Square: How many lines of symmetry does a square have?
Answer 4
Why 4.
The Rotation: A regular hexagon maps onto itself after a rotation of how many degrees, at minimum?
Answer 60 degrees
Why 60°.