Lesson 6 Justifying Constructions Practice Understanding

Ready

1.

What angles of rotational symmetry are there for a regular pentagon?

2.

What angles of rotational symmetry are there for a regular hexagon?

3.

If a regular polygon has an angle of rotational symmetry that is $40 °$ , how many sides does the polygon have?

On each given coordinate grid in problems 4 and 5, perform the indicated transformation.

4.

Reflect point $P$ over line $j$ .

5.

Rotate point $P$ $90 °$ clockwise around point $C$ .

Set

6.

Construct an isosceles triangle with $\overset{―}{C D}$ as the base and the other two sides not congruent to $\overset{―}{C D}$ . Explain why your construction works.

7.

Construct a regular hexagon with $\overset{―}{C D}$ as one of the sides. Construct the circumscribed circle around the hexagon. (Note: A circumscribed circle passes through all of the vertices of the polygon.)

8.

Construct a square with $\overset{―}{C D}$ as one of the sides. Construct the circumscribed circle around the square.

Go

9.

Which of all the geometric constructions is used the most or is most helpful when it comes to supporting the construction of other geometric constructions? Show this construction.

10.

Construct a parallelogram using the given line segments below as two of the sides.

11.

The sequence of transformations used frequently to show that figures are congruent is translate, rotate, and reflect, in that order. Why does this sequence make the most sense? Provide an example.

Find the slope of the line that passes through the given points. Then find the distance between the points. Show all your work.

12.

$(1, - 5), (- 7, 1)$

a.

Slope:

b.

Distance:

13.

$(- 10, 31), (20, 11)$

a.

Slope:

b.

Distance: