Day #2: Review

After a counterclockwise rotation about point X, scalene triangle ABC maps onto 

∆RST, as shown in the diagram below. Which statement must be true?

• ∠A≅∠R

• ∠A≅∠S

• CB≅TR

• CA≅TS

Answer explanation

A rigid motion, such as a rotation, does not change size, so the corresponding angles and sides remain the same.

The regular polygon below is rotated about its center. Which angle of rotation will carry the figure onto itself?

•  60°

• 108°

• 216°

• 540°

Answer explanation

One full rotation is 360 degrees. A regular pentagon will carry onto itself every 1/5th of a rotation. 360 / 5 = 72 degrees. So, this will happen at any multiple of 72 degrees.

In the diagram below, line m is parallel to line n. Figure 2 is the image of Figure 1 after a reflection over line m. Figure 3 is the image of Figure 2 after a reflection over line n. Which single transformation would carry Figure 1 onto Figure 3?

• a dilation

• a rotation

• a reflection 

• a translation

Answer explanation

A translation will move Figure 1 directly to Figure 3. Reflecting the figure switched the orientation, but reflecting it a second time switched it back to its original orientation.

Triangle A'B'C' is the image of triangle ABC after a translation of 2 units to the right and 3 units up.  Is 

∆ABC congruent to ∆A'B'C'?  Explain why.

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Answer explanation

Given square RSTV, where RS = 9 cm. If square RSTV is dilated by a scale factor of 3 about a given center, what is the perimeter, in centimeters, of the image of RSTV after the dilation?

•  12

• 27

• 36

• 108

Answer explanation

If RS = 9, then the perimeter is 9*4 = 36. If the square is dilated by a factor of 3, then the perimeter will be 3 times as much.

So 36 *3 =108.Alternatively, 9*3 = 27 cm as the length of the side of the image, and 27 *4 = 108.

Line MN is dilated by a scale factor of 2 centered at the point 

(0,6).  If MN is represented by y=-3x+6 , which equation can represent M'N', the image of MN?

• y=-3x+12

• y=-3x+6

• y=-6x+12

• y=-6x+6

Answer explanation

A dilation would not change the slope of a line, so eliminate Choices (3) and (4).A dilation would only change the y-intercept UNLESS the line goes through the center of dilation -- that is, if the center of dilation is a point on the line. In that case, the line remains unchanged because the image of every point will still fall on the same line.

Points

D(1,2), B(1,4), and C( 3,4) are graphed on the set of axes below. State the coordinates of D', the image of ∆DBC, after a dilation of scale factor 2.

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Answer explanation

Quadrilaterals BIKE and GOLF are graphed on the set of axes below. Describe a sequence of transformations that maps quadrilateral BIKE onto quadrilateral GOLF.

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The diagram below shows parallelogram ABCD with diagonals. 

AC and BD intersecting at E. What additional information is sufficient to prove that parallelogram ABCD is also a rhombus?

• BD bisects AC

• AB is parallel to CD

• AC is congruent to BD

• AC is perpendicular to BD

Answer explanation

The diagonals of a rhombus are perpendicular to each other.

Given: Parallelogram ABCD, 

BFAFD, and DEBEC

Prove:  BEDF is a rectangle

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Answer explanation

A rectangle is a parallelogram that contains a right angle.