Transformations and Parallel Lines
- Author:
- Rachel Fruin
- Topic:
- Geometry, Straight Lines
This applet lets you explore congruent angles formed by parallel lines with transformations.
1) Are the lines parallel? How do you know?
2) Drag points B and C to show that lines remain parallel.
3) Click “Step 1.” What transformation maps <HBD onto <H’BD’?
a) 180o Rotation b) Reflection c) Translation
4) Click “Step 2.” What transformation maps <D’BH’ onto <D”CH”?
a) 180o Rotation b) Reflection c) Translation
5) Click “Step 3.” What transformation maps <D”CH” onto <D’’’CH’’’?
6) a) 180o Rotation b) Reflection c) Translation
7) Drag points B and C to show that angles remain congruent. Drag points D and H to show that the transformations maintain congruence.
EXAMPLE: Write a paragraph proof. Prove that <1 is congruent to <3 using transformations.
A 180o Rotation maps <1 onto <2 therefore <1 <2. A translation maps <2 onto <3 therefore <2 <3. By transitive property <1 s congruent to <3.
8) Write a paragraph proof, using transformations, proving <2 s congruent to <4.