Congruence and Transformations

Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?

• $A\cong B\ and\ B\cong C$

• $A\cong A,\ B\cong B,\ C\cong C$

• Each triangle is a right triangle.

• Each triangle is an isosceles triangle.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Triangle GHI is rotated 90 degrees clockwise and then reflected over the y-axis. Which congruency statement is true?

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Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Ethan created three triangles: triangle X, triangle Y, and triangle Z. If 

 $\Delta Y\cong\Delta X\ \ \ and\ \ \ \ \Delta Y\cong\Delta Z$  
which must also be true?

• The triangles are equilateral.

• The triangles are right triangles.

• Triangles X and Z are congruent.

• Triangles X, Y, and Z share one or more vertices.

Tags

CCSS.8.G.A.2

Triangle ABC is shown with four images that are each the result of a transformation of triangle ABC.

For which triangle is one reflection necessary for the transformation to occur?

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Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

 $ABCD\cong FGHI\cong JKLM\cong NOPQ\cong RSTU$  

Square ABCD is shown with four congruent images such that.

For which square is a reflection necessary to produce the transformed figure?

• FGHI

• JKLM

• NOPQ

• RSTU

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

Figure G is rotated 90 degrees clockwise about the origin and then reflected over the x-axis, forming figure H.

Which sequence of transformations will produce the same results?

• a reflection over the y-axis and then a rotation 90 degrees clockwise about the origin

• a reflection over the x-axis and then a rotation 90 degrees clockwise about the origin

• a 180 degree rotation about the origin

• a reflection over the y-axis and then a reflection over the x-axis

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Harley graphs a polygon that is located entirely inside quadrant I. He rotates the figure clockwise 90 degrees about the origin and then reflects the rotated figure over the x-axis. He translates the resulting figure 3 units to the left and 3 units up. Which best describes the location of the final image?

• quadrant I

• quadrant II

• above the x-axis

• left of the y-axis

Tags

CCSS.8.G.A.1

CCSS.8.G.A.3

Triangle ABC is rotated 180º using the origin as the center of rotation.

Which sequence of transformations will produce the same result?

• a translation up 4 and then a reflection over the y-axis

• a translation up 4 and then a translation right 6

• a reflection over the x-axis and then a reflection over the y-axis

• a translation right 6 and then a reflection over the x-axis

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Figure X is translated down 5 and then reflected over the y-axis, forming figure Y.

Which sequence of transformations results in the same transformation?

• a translation left 5 units and then a reflection over the x-axis

• a translation left 5 units and then a translation down 5 units

• a 180 degree rotation using the origin as the center of rotation

• a reflection over the y-axis and then a translation down 5 units

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Which sequence of transformations produces A’B’C’ from ABC?

• a translation up 3 and then a 90º counterclockwise rotation about the origin

• a 90º counterclockwise rotation about the origin and then a translation up 3

• a reflection over the x-axis and then a translation left 2 and down 1

• a translation left 5 and down 2 and then a reflection over the x-axis

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3