Constructions and Rigid Transformations

You may use construction tools. This diagram is a straightedge and compass construction. C is the center of both circles. Select all statements that must be true by construction. (2 answers)

• 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.

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.

Priya followed this set of instructions to make quadrilateral ACBD. 1) Draw 2 points A and B 2) Draw a circle centered at A with radius AB 3) Draw a circle centered at B with radius AB 4) Label the intersection points of the circles C and D 5) Draw segments AC, BC,AD and BD Choose a description you can be sure is accurate for the shape she constructed.

• 2 congruent sides, but not all 4

• 4 congruent angles

• 4 congruent sides

• 4 congruent sides and 4 congruent angles

Triangle ABC is isosceles. Which tool is used to construct the perpendicular bisector for segment AB?

• Protractor

• Straightedge and compass

• Ruler

• Divider

Which of the following describes the sequence of transformations shown?

• Reflect across the x-axis and then rotate -90 degrees around the origin

• Rotate -90 degrees around the origin and then translate down.

• Reflect across the x-axis and then reflect across the y-axis.

• Translate up and then rotate 90 degrees about the origin.

Which of the following statements is true about each pair of lines in this construction? (3 answers)

• The lines j and i are parallel

• The lines i and g are perpendicular.

• The lines are intersecting at an angle.

• The lines j and g are perpendicular

Select the sequence of transformations that will take Polygon P to Polygon Q.

• Rotate 180 degrees about point A.

• Translate so that A is taken to J. Then reflect over BA.

• Rotate 60 degrees counterclockwise around A, then reflect over FA.

• Reflect over line BA, then rotate 60 degrees counterclockwise about point A.

Select all sequences of translations, rotations, and reflections below that would take polygon P to polygon Q .

• Translate so that A is taken to J. Then reflect over line BA

• Reflect over line BA and then translate by directed line segment BA

Which image shows the construction of a perpendicular bisector?

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Which of the following shows the construction of an angle bisector?

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