Congruency

What does congruent mean?

• same shape different size

• Same size and shape

• same geometric angles

• equal measurement

Trapezoid PQRS is rotated 180° about the origin to form trapezoid P'Q'R'S'. Which statement is true?

• The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid P'Q'R'S'.

• Trapezoid PQRS is not congruent to trapezoid P'Q'R'S'.

• The area of trapezoid PQRS is less than the area of trapezoid P'Q'R'S'.

• The angle measures of trapezoid PQRS are equal to corresponding angle measures of trapezoid P'Q'R'S'.

Pentagon ABCDE is rotated 180° clockwise about the origin to form pentagon A'B'C'D'E'. Which statement is true?

• Pentagon ABCDE is congruent to pentagon A'B'C'D'E'.

• The sum of the angle measures of pentagon A'B'C'D'E is 180° more than the sum of the angle measures of pentagon ABCDE.

• Each side of pentagon A'B'C'D'E' is 2 times the corresponding side length of pentagon ABCDE.

• Each side of pentagon A'B'C'D'E' is 1/2 the corresponding side length of pentagon ABCDE.

Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the origin as the center of dilation using the rule (x, y)→(1/4x, 1/4y) to create pentagon M'N'P'Q'R'.

Which statement is true?

• Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.

• Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1.

• Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.

• Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.

Tags

CCSS.8.G.A.3

CCSS.8.G.A.4

Quadrilateral PRST is transformed according to the rule (x, y)--(x + 9, y + 4) to create quadrilateral P'R'S'T'. Which statement is true?

• The side lengths of quadrilateral P'R'S'T' are twice the corresponding side lengths of quadrilateral PRST.

• The angle measures of quadrilateral P'R'S'T' are equal to the corresponding angle measures of quadrilateral PRST.

• The side lengths of quadrilateral P'R'S'T' are 9 units longer than the corresponding side lengths of quadrilateral PRST.

• The angle measures of quadrilateral P'R'S'T' are greater than the corresponding angle measures of quadrilateral PRST.

Which representation of a transformation on a coordinate grid does not preserve congruence?

• (x, y)→(1/7x, 1/7y)

• (x, y)→(x + 7, y + 7)

• (x, y)→(x, -y)

• (x, y)→(y, -x)

A transformation is applied to a figure to create a new figure. Which transformation does not preserve congruence?

• A reflection across the x-axis

• A translation 7 units down

• A dilation by a scale factor of 5.

• A rotation of 90⁰ clockwise

A triangle in Quadrant I is shown below. Which transformation would create a new triangle that is not congruent to the given triangle?

• Translation of 4 units left and 2 units down.

• Reflection across the x-axis

• Dilations of a scale factor of 3.

• Rotation of 90 degrees clockwise about the origin.

Which table correctly organizes transformations into those that always preserve congruence and those that may not always preserve congruence?

• 
• 
• 
• 

Which representation of a transformation on a coordinate grid does NOT preserve congruency?

• (x,y) —›(34x, 34y)

• (x,y) —›(x, -y)

• (x,y) —›(x + 34, y + 34)

• (x,y) —›(y, -x)