Congruence and Transformations Answers

Jason states that . Kelley states that . Which best describes the accuracy of the congruency statements?

Figure G is rotated 90 clockwise about the origin and then reflected over the x-axis, forming figure H. Which sequence of transformations will produce the same results?

Ethan created three triangles: triangle X, triangle Y, and triangle Z. If and , which must also be true?

Which sequence of transformations produces R’S’T’ from RST?

Harley graphs a polygon that is located entirely inside quadrant I. He rotates the figure clockwise 90 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?

A teacher asks students to determine the accuracy of this statement.A reflection over the x-axis and then over the y-axis results in the same transformation as a 180 rotation about the origin of the original figure.Kwame’s explanation of the accuracy of the statement is shown below.Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3). Step 2: Reflect the pre-image over the x-axis: (1, –2), (1, –4), (2, –3).Step 3: Reflect the figure from step 2 over the y-axis: (–1, 2), (–1, 4), (–2, 3).Step 4: Rotate the pre-image 180: (–1, –2), (–1, –4), (–2, –3).Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate.Which best explains Kwame’s solution?

Triangle MNO is rotated 180 using the origin as the center of rotation. Which sequences of transformations will produce the same results? Check all that apply.

The vertices A(–2, –1), B(–3, 2), C(–1, 3), and D(0, 0) form a parallelogram. The vertices A’(–1, –2), B’(2, –3), C’(3, –1), and D’(0, 0) are the image of the parallelogram after a sequence of transformations. Which sequence of transformations could produce the image from the pre-image?

Square ABCD is shown with four congruent images such that ABCD FGHI JKLM NOPQ RSTU. For which square is a reflection necessary to produce the transformed figure?