1. Chapter 7 Geometry
Homework Answers

2. Sec 7.1 Rigid; reflected, but the size and the shape do not change.
Nonrigid; the shape changes.
Nonrigid; the size changes.
see diagram
a. Sample answer: Fold the paper so that the images coincide, and crease.
b. Construct a segment that connects two corresponding points. Construct the perpendicular bisector of that segment.
a. Extend the three horizontal segments onto the other side of the reflection line. Use your compass to measure lengths of segments and distances from the reflection line.
b. see diagram
11. see diagram
12. Reflectional symmetry
13. 4-fold rotational and reflectional symmetry
14. Reflectional symmetry

3. Sec 7.2 translation; see diagram reflection; see diagram
rotation; see diagram
Rules that involve x or y changing signs produce reflections. Rules that produce translations involve a constant being added to the x and/or y terms. If both x and y change signs, the rule produces a rotation.
(x,y) → (x,-y)
(x,y) → (-x,-y)
One, unless it is equilateral, in which case it has three.
Two, unless it is a square, in which case it has four.

4. Sec 7.3
(10,10)
A 180° rotation. If the centers of rotation differ, rotate 180° and add a translation.
a. 20 cm
b. 20 cm, but in the opposite direction
a. 80° counterclockwise
b. 80° clockwise
180°
3 cm
see diagram

5. Sec 7.4
3³.4²
3⁴.6
3².4.3.4
/3.4².6
3³.4²/3².4.3.4
3⁶/3².4.12

6. Sec 7.6 regular hexagons squares or parallelograms see diagram
Answers will vary

7. Sec 7.7 equilateral triangles regular triangles see diagram
Answers will vary
False; they must bisect each other in a parallelogram.
true
False; it could be kite or an isosceles trapezoid.
The path would be ¼ of Earth’s circumference, approximately 6280 miles, which will take 126 hours, or around 5¼ days.

8. Sec 7.8
parallelograms
see diagram
Answers will vary

9. Ch 7 Review
true
False; a regular pentagon does not create a monohedral tessellation and a regular hexagon does.
False; two counterexamples are given in Lesson 7.5
False; any hexagon with all opposite sides parallel and congruent will create a monohedral tessellation.
3⁶/3².4.3.4; 2-uniform
4.8²; semiregular
Use a grid of squares. Tessellate by translation.
Use a grid of equilateral triangles. Tessellate by rotation.
Use a grid of parallelograms. Tessellate by glide reflection.