Question

Problem 1) Find the scale factor of dilation for the triangles below.



(1 point)
Responses

k = 1
k = 1

k = 2
k = 2

k = 5
k = 5

k = 8
k = 8
Question 2
Problem 2) What scale factor of dilation could we use to create the red line from the black line? Hint: you must first use the distance formula to find the length of the lines.



(1 point)
Responses

k = 3
k = 3

k = 4
k = 4

k = 0.5
k = 0.5

k = 2.5
k = 2.5
Question 3
Problem 3) Find the coordinates of point X on segment PQ that partitions the segment into a ratio such that PX:XQ = 2:1.



(1 point)
Responses

(4,2)
(4,2)

(1,3)
(1,3)

(0,5)
(0,5)

(9,3)
(9,3)
Question 4
Problem 4) Suppose we dilate this triangle by a factor of k = 2. What will be the new coordinate of A'?



(1 point)
Responses

A' = (4,6)
A' = (4,6)

A' = (5,1)
A' = (5,1)

A' = (8,9)
A' = (8,9)

A' = (1,2)
A' = (1,2)
Question 5
Problem 5) Suppose we dilate this triangle by a factor of 3. What would be the new coordinate of point X'?



(1 point)
Responses

X' = (1,5)
X' = (1,5)

X' = (6,12)
X' = (6,12)

X' = (8,3)
X' = (8,3)

X' = (0,4)
X' = (0,4)
Question 6
Problem 6) What type of transformation uses a scale factor to change the size of a figure?(1 point)
Responses

Reflection
Reflection

Translation
Translation

Rotation
Rotation

Dilation
Dilation
Question 7
7) What theorem could we use to prove these triangles are similar?



(1 point)
Responses

AA~ Theorem
AA~ Theorem

SAS~ Theorem
SAS~ Theorem

SSS~ Theorem
SSS~ Theorem

Vertical Angles Theorem
Vertical Angles Theorem
Question 8
Problem 8) Use the Triangle Proportionality Theorem to calculate the value of x.



(1 point)
Responses

x = 5
x = 5

x = 3
x = 3

x = 1
x = 1

x = 10
x = 10
Question 9
Problem 9) Use the Triangle Midsegment Theorem to calculate the length of segment MN.



(1 point)
Responses

MN = 2
MN = 2

MN = 5
MN = 5

MN = 10
MN = 10

MN = 20
MN = 20
Question 10
Problem 10) Suppose these triangles are similar. Use proportions to find the value of x.



(1 point)
Responses

x = 5
x = 5

x = 12
x = 12

x = 20
x = 20

x = 11
x = 11
Question 11
Problem 11) Suppose this rectangle is dilated by a scale factor of 2. What is the area of the dilated rectangle?



(1 point)
Responses

A = 84
A = 84

A = 21
A = 21

A = 32
A = 32

A = 30
A = 30
Question 12
Problem 12) Suppose we have these two similar squares that are related by a scale factor of k = 4. What is the ratio of their areas? (hint: ratio = bigger square/smaller square)





(1 point)
Responses

Ratio = 3
Ratio = 3

Ratio = 12
Ratio = 12

Ratio = 16
Ratio = 16

Ratio = 10
Ratio = 10
Question 13
Problem 13) Suppose we have a rectangle with an area of A = 21 (pictured below). If we dilate this rectangle by a linear scale factor of k = 2, what will be the new area?



(1 point)
Responses

A = 35
A = 35

A = 84
A = 84

A = 91
A = 91

A = 67
A = 67
Question 14
Problem 14) Suppose we have a rectangle with a volume of 120 (pictured below). If we dilate this rectangle by a linear scale factor of k = 2, what would be the new volume?





(1 point)
Responses

V = 960
V = 960

V = 120
V = 120

V = 60
V = 60

V = 600
V = 600
Question 15
Problem 15) Suppose we have a triangular prism with volume of V = 42 (pictured below). If we dilate this figure by a linear scale factor of k=3, what would be the new volume?



(1 point)
Responses

V = 786
V = 786

V = 810
V = 810

V = 1134
V = 1134

V = 960
V = 960
Question 16
Problem 16) Use the geometric mean to calculate the value of x in this right triangle.



(1 point)
Responses

x = 2
x = 2

x = 6
x = 6

x = 1
x = 1

x = 10
x = 10
Question 17
Problem 17) Use the geometric mean to calculate the value of x in this right triangle.



(1 point)
Responses

x = 4
x = 4

x = 7
x = 7

x = 8
x = 8

x = 9
x = 9
Question 18
Problem 18) In the space below, please describe whether the SAS~, SSS~ or AA~ theorems can be used to prove these triangles are similar. Explain the reasoning behind your answer.



(3 points)
0 / 10000 Word Limit
Question 19
Problem 19) In the space below, please describe whether the SAS~, SSS~ or AA~ theorems can be used to prove these triangles are similar. Explain the reasoning behind your answer.



(3 points)
0 / 10000 Word Limit
Question 20
Problem 20) In the space below, please describe whether the SAS~, SSS~ or AA~ theorems can be used to prove these triangles are similar. Explain the reasoning behind your answer.





(3 points)

Answer 1

I can help — but I can’t see the diagrams or numbers you used in the quiz. Please either upload the images or give the needed coordinates/lengths for each problem. Below I list (1) which problems I can answer without the pictures and their answers, (2) the exact data I need for the remaining problems, and (3) short step-by-step methods so you (or I, once you provide the missing info) can get the correct answers quickly.

Answers I can determine now
- Question 6: Dilation (a dilation is the transformation that uses a scale factor to change size).
- Question 7: AA~ Theorem is the most common theorem to prove two triangles similar when two pairs of corresponding angles are congruent. (SAS~ and SSS~ also prove similarity but require side-angle-side or three corresponding sides proportional.)
- Question 12: Ratio = 16. For squares (or any similar plane figures) the ratio of areas = k^2. If k = 4 then area ratio = 4^2 = 16.
- Question 13: A = 84. Area scales by k^2; k = 2 gives factor 4, so new area = 21 × 4 = 84.
- Question 14: V = 960. Volume scales by k^3; k = 2 gives factor 8, so new volume = 120 × 8 = 960.
- Question 15: V = 1134. Volume scale factor = 3^3 = 27, so new volume = 42 × 27 = 1134.

What I need for the other questions (upload or type these)
- Q1 (scale factor of dilation for triangles): give the side lengths of each triangle or coordinates of corresponding vertices.
- Q2 (scale factor for a red line from a black line): give the endpoints of each line so I can compute lengths (distance formula) and ratio.
- Q3 (point X on PQ with PX:XQ = 2:1): give coordinates of P and Q (then I’ll compute X).
- Q4 (dilate triangle by k = 2, find A'): give coordinates of A and the center of dilation (if not given assume origin).
- Q5 (dilate by k = 3, find X'): give coordinates of X and center of dilation.
- Q8 (Triangle Proportionality Theorem to find x): give the diagram lengths or the numeric labeled segments.
- Q9 (Triangle Midsegment Theorem): give the lengths shown in the diagram (midsegment equals half the third side).
- Q10 (use proportions to find x): give the side lengths or diagram.
- Q11 (dilate rectangle by 2 find new area): give original rectangle dimensions or area (if area given, new area = original × 4).
- Q16 & Q17 (geometric mean problems in right triangles): give the diagram labels (hypotenuse/segments or legs) or the numbers shown so I can compute x using the geometric mean relationships.
- Q18–Q20 (explain which similarity theorem applies): upload each triangle diagram or list which angles and/or sides are marked congruent or proportional.

Quick formulas / methods to use (so you can solve or I can compute after you send data)
- Scale factor from two corresponding side lengths: k = (length in image 2) / (length in image 1).
- Distance formula for segment AB: d = sqrt((x2 − x1)^2 + (y2 − y1)^2).
- Internal partition (divide PQ so PX:XQ = 2:1): X = P + (2/3)(Q − P) = ((1*Px + 2*Qx)/3, (1*Py + 2*Qy)/3).
- Dilation about origin: (x,y) → (k x, k y). If center of dilation is not origin C = (cx,cy), then A' = C + k(A − C).
- Area scaling: area' = k^2 × area.
- Volume scaling: volume' = k^3 × volume.
- Triangle similarity theorems:
- AA~: two angles congruent → triangles similar.
- SAS~: included angles congruent and sides around angle proportional → similar.
- SSS~: all three sides proportional → similar.
- Geometric mean in right triangles (altitude to hypotenuse):
- If altitude from right angle divides hypotenuse into segments p and q, and hypotenuse = p+q:
- altitude h = sqrt(pq)
- each leg: e.g. leg a = sqrt(p(p+q)) or a^2 = p(p+q)
- or a^2 = hypotenuse × adjacent segment

If you upload the images or paste the numeric info for each question, I’ll finish the quiz answers and show step-by-step work for each one.