TNReady Congruence Problems

• Reflection of Triangle ABC over the line y=x

• Translation of Triangle ABC 7 units right and 9 units down

• Rotation of Triangle ABC 90 degrees clockwise, centered at the origin

• Reflection of Triangle ABC over the y-axis and then over the x-axis

Triangle RST is translated 5 units left and 3 units down and then reflected over the line y=x. Triangle JKL is congruent to the final image of Triangle RST. Select all statements that must be true.

• Triangle RST is congruent to Triangle JKL

• There is a sequence of transformations that would map Triangle JKL to Triangle RST.

• Angle K is congruent to an angle of Triangle RST.

• Triangle JKL is similar to Triangle RST with a scale factor of 8.

• The perimeter, in cm, of Triangle JKL is equal to 2 more than the perimeter, in cm, of Triangle RST.

The rectangle shown is reflected over the x-axis, and then, after a second transformation, the final image is mapped back onto the original figure. Which could NOT have been the second transformation?

• rotation 90 degrees clockwise

• rotation 180 degrees clockwise

• reflection over the x-axis

• reflection over the y-axis

Aniyah has repeatedly stenciled the triangle shape shown on her bedroom wall. Her best friend wants to copy the exact same shape on her bedroom wall. Which statement has sufficient information about the triangle for Aniyah to give to her friend to guarantee that she will have the exact same triangle?

• Construct a triangle with angle degrees 33, 42, and 105.

• Construct a triangle with sides 22 inches and 27 inches where the included angle is 105 degrees.

• Construct a triangle with sides 39 inches and 22 inches and a non-included angle of 33 degrees.

• Construct a triangle with a 105 degree angle opposite from a side of 39 inches where the remaining 2 sides differ in length by 5 inches.

The triangles QTP and SPT are shown. Line RM is the perpendicular bisector of line segment PT and intersects line segment PT at point M.

Which transformation would imply that Triangle QTP is congruent to Triangle SPT?

• horizontal translation the length of segment PR

• horizontal translation the length of segment PT

• reflection over ray MR

• reflection over segment SP

What is the reason for statement 5?

• AAS

• ASA

• SAS

• SAS

Triangle RST with vertices R(-1,3), S(4,2), and T(3,-4) is rotated 90 degrees counterclockwise about the origin.

What are the images of the vertices of the triangle?

• R'(-3,-1), S'(-2,4), and T'(4,3)

• R'(1,-3), S'(-4,-2), and T'(-3,4)

• R'(3,-1), S'(2,4), and T'(-4,3)

• R'(-1,-3), S'(4,-2), and T'(3,4)

Trapezoid RSTU is shown. Write the equation for the line that would map the trapezoid onto itself.

• x = 2

• y = 2

• x= -1

• y = -6/5x + 12/5

Triangle ABC has vertices A(-3,3), B(2,4), and C(-2,2) and is translated according to the rule (x,y) maps to (x+2, y-4).

What are the coordinates of the vertices of the translated figure?

• A'(-7,5), B'(-2,6), and C'(-6,4)

• A'(-1,-1), B'(4,0), and C'(0,-2)

• A'(-5,7), B'(0,8), and C'(-4,6)

• A'(-1,-1), B'(6,-2), and C'(4,-6)