Question

24)

Draw a line segment of any length and label it PQ.
If you were to construct a line segment congruent to PQ, what would be your first step?
A) Put one end of the compass on point P and the other end on point Q.
B) Measure PQ using a ruler.
C) Draw an arc the size of PQ below the segment.
D) Draw a new segent below the line the same length as PQ.
25)

Describe the transformation that maps the pre-image A to the image A'.
A) translated 10 units to right and then 10 units up
B) translated 5 units to left and then reflected across the x-axis
C) translated 10 units to right and then reflected across the x-axis
D) translated 10 units to right and then reflected across the y-axis
26) Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left and 4 units up. Finally, he reflects the image over the line x = 1. Are the original and transformed images congruent? Justify your answer.
A) no; Two reflections will change the size of the original image.
B) no; Reflections and translations are fluid motions. Fluid motions change the size of the original image.
C) yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.
D) yes; Reflections and translations are fluid motions. Fluid motions preserve the size of the original image.
27) Given a rectangle with a length of 36 and a width of 9, which rectangle is similar?
A) rectangle with a length of 30 and a width of 6
B) rectangle with a length of 44 and a width of 11
C) rectangle with a length of 64 and a width of 8
D) rectangle with a length of 72 and a width of 12
28)

Given that these two figures are similar, what is the measure of the unknown angle?
A) 34°
B) 56°
C) 68°
D) 112°
29)

By which rule are these triangles congruent?
A) AAS
B) ASA
C) SAS
D) SSS
30)

Given that the two figures are similar, what scale factor can be used to find the missing length x?
A) 6
13

B) 1
2

C) 5
6

D) 2
31)

Which statement is true?
A) Since B is on the perpendicular bisector of AB and ∠ADB is a right angle, BD is the perpendicular bisector of AD.
.
B) Since B is on the perpendicular bisector of AC and ∠CDB is a right angle, BD is the perpendicular bisector of CD.
C) Since B is on the perpendicular bisector of AC and ∠ADB is a right angle, BD is the perpendicular bisector of AD.
.
D) Since B is on the perpendicular bisector of AC and ∠ADB is a right angle, BD is the perpendicular bisector of AC.
.
32)

An isosceles triangle is shown. Which two angles must be congruent?
A) ∠V ≅ ∠W
B) ∠V ≅ ∠X
C) ∠W ≅ ∠X
D) Cannot be determined

*Attachments are in order and are used for 28,29,30,31 and 32

Answer 1

24) A

25) picture is missing

26) C

27) B

28) C

29) D

30) D

31) D

32) A

Explanation:

24) You have to put one end of the compass on point P and the other end on point Q, so that, you have the measure of the segment.

25) The figure is missing, so I will answer the question in general terms.

• translation 10 units to right and then 10 units up transforms point (x, y) into (x +10, y+10)

• translation 5 units to left and then reflected across the x-axis transforms point (x, y) into (x-5, -y)

• translation 10 units to right and then reflected across the x-axis transforms point (x, y) into (x+10, -y)

• translation 10 units to right and then reflected across the y-axis transforms point (x, y) into (-x-10, y)

26) yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.

27) The ratio length/width must be the same

original case: 36/9 = 4

A) 30/6 = 5

B) 44/11 = 4

C) 64/8 = 8

D) 72/12 = 6

28) The angle '?' must be equal to the acute angle of the original figure

29) As shown in the picture, three sides are equal

30) The following proportion must be satisfied:

12/6 = 13/y = 5/x = 2, which is the scale factor

31) Since B is on the perpendicular bisector of AC and ∠ADB is a right angle, BD is the perpendicular bisector of AC. All of these is shown in the picture

32) ∠V ≅ ∠W. This is a property of isosceles triangles