End of Unit 1 Assessment: Illustrative Math Geometry

Select all the figures with 180-degree rotation symmetry.

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Select the construction that guarantees

A′ is a reflection of point A across line BC.

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ABCD is a rectangle.

Trapezoid AEFB is congruent to trapezoid CFED.

G is the midpoint of segment EF.

Select all 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.

Answer explanation

The rigid transformations that take trapezoid AEFB to CFED include rotating 180 degrees around point G (both clockwise and counterclockwise) and translating AEFB from F to E, then rotating around point E.

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

What is the image of segment BC after a 120-degree clockwise rotation about point H?

• Segment DE

• Segment CD

• Segment AF

• Segment AB

Answer explanation

A 120-degree clockwise rotation of segment BC around point H moves point B to point A and point C to point F. Thus, segment BC transforms into segment AF.

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

What is the image of segment BC after a reflection over line FC?

• Segment DE

• Segment CD

• Segment AF

• Segment AB

Answer explanation

Reflecting segment BC over line FC results in segment CD. This is because in a regular hexagon, segments opposite each other are congruent and symmetric with respect to the lines connecting their vertices.

Which transformation carries the parallelogram below onto itself?

• a reflection over y = x

• a reflection over y = -x

• a rotation of 90° counterclockwise about the origin

• a rotation of 180° counterclockwise about the origin

Answer explanation

A rotation of 180° counterclockwise about the origin maps each vertex of the parallelogram to its opposite vertex, thus carrying the shape onto itself. The other transformations do not preserve the shape's orientation.

What type of triangles are ABC and DEF as shown in the diagram?

• Similar

• Congruent

• Isosceles

• Scalene

Answer explanation

Triangles ABC and DEF are congruent because they have the same size and shape, meaning all corresponding sides and angles are equal. This makes them identical in every aspect, confirming the correct choice.

What is the task described in the problem regarding triangles ABC and DEF?

• Calculate the area of triangle ABC

• Describe a sequence of rigid motions that maps ABC onto DEF

• Find the perimeter of triangle DEF

• Determine the angles of triangle ABC

Answer explanation

The task involves finding a sequence of rigid motions (like translations, rotations, and reflections) that can transform triangle ABC into triangle DEF, indicating a focus on congruence rather than measurements.

If triangle ABC is translated to map onto triangle DEF, which point corresponds to point A?

• Point D

• Point E

• Point F

• Point C

Answer explanation

In a translation, corresponding points maintain their relative positions. Since triangle ABC maps onto triangle DEF, point A corresponds to point D, making it the correct answer.

Which transformation involves flipping a figure over a line?

• Translation

• Rotation

• Reflection

• Dilation

Answer explanation

The transformation that involves flipping a figure over a line is called a reflection. In reflection, each point of the figure is mirrored across the line, creating a symmetrical image.