01 Constructions & Congruence

Select all the figures with 180˚ rotation symmetry.

• Image A: right, isosceles triangle

• Image B: Rectangle

• Image C: Square

• Image D: Regular pentagon

• Image E: Regular hexagon

Tags

CCSS.HSG.CO.A.4

Select the construction that guarentees A' is a reflection of point A across line BC.

• Construction A

• Construction B

• Construction C

• Construction D

Tags

CCSS.HSG.CO.B.6

ABCD is a rectangle. Trapezoid AEFB is congruent to trapezoid CFED. G is the midpoint of segment EF.

Select all of the ways we could describe the rigid transformation that takes AEFB to CFED.

• Reflect AEFB across line EF

• Rotate AEFB 180 degrees counterclockwise around point G.

• Rotate AEFB 180 degrees clockwise around point G.

• Translate AEFB by the directed line segment from F to E, and then reflect across line FE.

• Translate AEFB by the directed line segment from F to E, and then rotate 180 degrees clockwise around point E.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Regular hexagon ABCDEF is inscribed in a circle with center H.

a. If only segment BC is rotated 120˚ clockwise, what side of the hexagon would BC land on?

b. What would be the image of segment BC after a reflection over line FC?

Tags

CCSS.8.G.A.3

Describe a sequence of transformations that take isosceles trapezoid T to its image T'.

Tags

CCSS.8.G.A.3

This diagram is a straightedge and compass construction. C is the center of both circles.

Select all statements that must be true by construction.

• Segments AB and AD have the same length

• Segments AC and AD have the same length

• Segments AC and CD have the same length

• Triangle BCE is isosceles

• Triangle CDE is isosceles

Tags

CCSS.HSG.CO.C.9

Line CD is the perpendicular bisector of segment AB. The lines intersect at point E. Which of these statements is true?

• E is closer to A.

• E is closer to B.

• E is the same distance from A and B.

• There is not enough information to be sure.

Tags

CCSS.HSG.CO.C.9

Answer each question about each pair of lines in the construction.

What is the relationship of line i to line j ?_

What is the relationship of line i to line g ?_

What is the relationship of line g to line j? _

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

The three congruent circles in the diagram have centers A, B, and C.

a. Explain why segments AB and AC have the same length.

b. Classify triangle ABC. Justify your classification.

Tags

CCSS.HSG.SRT.B.5

A. Write the coordinates of the image.

B. Describe the transformation precisely.

C. Does the transformation result in a figure that is congruent to the original, similar to the original, both or neither?

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5