Constructions and Rigid Transformations: Mid-Unit Review

This diagram is a schematic of a construction using a straightedge and compass.

C is the center of both circles. Please select all statements that must necessarily be true based on the construction.

• Segments AB and AD are equal in length.

• Segments AC and AD are equal in length.

• Segments AC and CD are equal in length.

• Triangle BCE is an isosceles triangle.

• Triangle CDE is an isosceles triangle.

Tags

CCSS.HSG.CO.B.6

Line CD is the perpendicular bisector of segment AB.

The two lines intersect at point E. Which of the following statements is correct?

(Draw a diagram if necessary.)

• Point E is closer to A.

• Point E is closer to B.

• The distance from E to A is equal to the distance from E to B.

• There is not enough information to determine.

Tags

CCSS.HSG.CO.C.9

Priya drew a quadrilateral ACBD by following these steps.

Please choose an option that you can be sure accurately describes the figure she drew:

Step 1: Draw points A and B

Step 2: With A as the center and AB as the radius, draw a circle

Step 3: With B as the center and AB as the radius, draw a circle

Step 4: Mark the intersection points of the two circles as C and D

Step 5: Connect AC, BC, AD, BD

• There are two congruent sides, but not four

• There are four congruent angles

• There are four congruent sides

• There are four congruent sides and four congruent angles

Tags

CCSS.8.G.A.2

A circle is defined as:

• A closed curve where all points are at an equal distance from a fixed point.

• A shape with three straight sides.

• A polygon with four equal sides.

• A shape with no sides or angles.

5. In an isosceles triangle ABC, when using a ruler and compass to construct the perpendicular bisector of segment AB, which of the following steps is correct?

• With A and B as centers and the same radius, draw arcs so that the arcs intersect above and below AB, then connect the intersection points.

• Draw a line from point A to point C, then draw a line from point B to point C.

• Measure the length of AB and mark its midpoint, then draw a line perpendicular to AB through the midpoint.

• With A as the center and B as the radius, draw a circle, then with B as the center and A as the radius, draw a circle.

Tags

CCSS.HSG.CO.C.9

The lengths of segments AB and AC are equal because:

• They are both radii of the same circle.

• They are parallel to each other.

• They are perpendicular to each other.

• They are in different planes.

Classify triangle ABC. Please choose the most appropriate classification.

• Equilateral triangle

• Obtuse isosceles triangle

• Acute scalene triangle

• Right isosceles triangle

Tags

CCSS.4.G.A.2

Mai wants to construct a regular hexagon inside a circle centered at C. Starting from the given construction steps, can the following instructions complete the construction of a regular hexagon? If yes, explain why Mai is correct. If not, correctly complete the construction.

• Yes, because marking six points on the circle with the radius will always give a regular hexagon.

• No, because the points marked and connected will not form a regular hexagon.

• No, because you need to use a protractor to measure a 60-degree angle at each vertex.

• Yes, because any polygon can be inscribed in a circle using this method.

Tags

CCSS.HSG.CO.A.3

Fill in the blank:

In this figure, line i and line j are ________.

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

Fill in the blank:

In this figure, line i and line g are __________.

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1