question 11

carlos performed a transformation on trapezoid efgh to create e′f′g′h′, as shown in the figure below:

a four quadrant coordinate grid is drawn. trapezoid efgh with coordinates are drawn at e negative 6, negative 4. f is at negative 4, negative 4. g is at negative 2, negative 6. h is at negative 7, negative 7. trapezoid e prime f prime g prime h prime with coordinates are drawn at e prime negative 4, 6. f prime is at negative 4, 4. g prime is at negative 6, 2. h prime is at negative 7, 7.

what transformation did carlos perform to create e′f′g′h′?

a)rotation of 90° counterclockwise about the origin
b)rotation of 90° counterclockwise about the center of the figure
c)rotation of 90° clockwise about the origin
d)rotation of 90° clockwise about the center of the figure

question 12

jeremiah is working on a model bridge. he needs to create triangular components, and he plans to use toothpicks. he finds three toothpicks of lengths 4 in., 5 in., and 2 in. will he be able to create the triangular component with these toothpicks without modifying any of the lengths?

a)yes, according to the triangle inequality theorem
b)yes, according to the triangle sum theorem
c)no, according to the triangle inequality theorem
d)no, according to the triangle sum theorem

question 13

which of the following would be a line of reflection that would map abcd onto itself?

square abcd with a at negative 3 comma 0, b at negative 3 comma 2, c at negative 1 comma 2, and d at negative 1 comma 0.

a) y = 2
b) 3x + y = 1
c)3x + y = −1
d) −3x + 3y = 9

question 14

figure efgh on the grid below represents a trapezoidal plate at its starting position on a rotating platform:

trapezoid efgh with vertices e at negative 4 comma 8, f at negative 7 comma 5, g at negative 4 comma 3, and h at negative 2 comma 5.

the plate is rotated 90° about the origin in the counterclockwise direction. which of the following describes the relationship of the paths traced by f and g as they undergo this rotation?

a) they form concentric circles.
b) they form congruent segments.
c) they form parallel segments.
d) they form perpendicular segments.

question 15

look at the quadrilateral shown below:

a quadrilateral abcd is shown with diagonals ac and bd intersecting in point o. angle aob is labeled as 1, angle boc is labeled as 4, angle cod is labeled as 2, and angle aod is labeled as 3.

melissa writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:

melissa's proof

for triangles aob and cod, angle 1 is equal to angle 2, as they are vertical angles.
ao = oc and bo = od because it is given that diagonals bisect each other.
the are congruent by sas postulate.
similarly, triangles aod and cob are congruent.
by cpctc, ab is equal to dc.
by cpctc, ad is equal to bc.
as the opposite sides are congruent, the quadrilateral abcd is a parallelogram.

which is the missing phrase in melissa's proof?
a) angles adb and cbd
b) angles aob and cod
c)triangles adb and cbd
d) triangles aob and cod