Name_____________________________________________Date____________________Period__________ Worksheet: Section 7.1 Examples #1-4: Graph the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor. 1. 2. 3. 4. y x y x 2,4 , 3 4,4 , 3,2 ; 2 with vertices and JKP J K P k -2,4 , -2,-2 , -4, -2 -4, 2 ; 0.5 Trapezoid with vertices and ABCD A B C D k 4,4 , 3 0,0 , 8,0 ; 4 with vertices and DGF D G F k -2,0 , 0,2 , 2,-2 ; 3 with vertices and DGF D G F k y x y x
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Name_____________________________________________Date____________________Period__________ Worksheet: Section 7.3 β Part III
1.
2.
2, 8
3, 12
Given:
Prove:
AB BC
AE ED
BE CD
5, 2, 4
8, 15, 6
Given:
Prove:
WU WX UX
ZU YZ YX
W Y
3.
4.
Given: is a trapezoid
with bases &
Prove:
ABCD
AB DC
DP CP
PB PA
6, 4,
8, 3
Given:
Prove:
AC CD
BC CE
AB AC
ED EC
Name: __________________________
Unit 7 β Celebration of Knowledge Review β Day 1
For 1 β 2, solve each proportion.
1. 12 21
44 x 2.
40 3 1
27 2 1
x
x
1.___________
2. ___________ For 3 β 4, determine whether the two polygons are similar below. Justify your answer! 3.___________ 4.___________
8. Determine whether the triangles below are similar. If so, tell Which similarity is used and complete the statement (order counts). 8.____________________
15. If D, E, and F are the midpoints of their respective sides, complete the following statements.
For 18 β 20, draw and diagram using the given information and answer each question.
For 21 and 22, Find the value of the missing variable. 21. 22. 21._______________ 22._______________
For 26 β 30, use the diagram to the right. Determine the length of each segment.
30. AE 31. ED 32. Perimeter Ratio 33. A right angle is divided into two angles whose measures are in the ratio of 2 to 7. Find the measure of the smaller angle. 34. The ratio of the measures of the angles of a triangle is 2:2:14. What is the measure of each angle?
Unit 7 β Celebration of Knowledge Review #2 1. The triangles shown are similar. Which of the following is not a correct statement?
A.
π΄π΅
ππ=
π΅πΆ
ππ C.
πΆπ΄
ππ=
π΅π΄
ππ
B. π΅πΆ
ππ=
π΄πΆ
ππ D.
π΄πΆ
ππ=
π΄π΅
ππ
2. On the coordinate grid below, one triangle is drawn and two vertices for a second triangle are also
shown. Which coordinates for the third vertex will form another triangle that is similar to the one
drawn?
A. (6, β1)
B. (6, β7)
C. (7, β1)
D. (10, β1)
3. Find the length of ππΜ Μ Μ Μ in the diagram below.
A. ππ = 5
B. ππ = 6
C. ππ = 8
D. ππ = 18
4. What is the value of x in the figure below?
A. π₯ = 4
B. π₯ = 5
C. π₯ = 6
D. π₯ = 7
5. What is the value for π₯ ?
A. π₯ = 18
B. π₯ = 16
C. π₯ = 12
D. π₯ = 3
6. In the figure below, what is the length of π΄π΅Μ Μ Μ Μ ?
A. π΄π΅ = 7
B. π΄π΅ = 11
C. π΄π΅ = 16
D. π΄π΅ = 20
7. Two triangles are similar and the ratio of each pair of corresponding sides is 2: 1 . Which
statement regarding the two triangles is not true?
A. Their perimeters have a ratio of 2: 1
B. The scale factor is a ratio of 2: 1
C. Their corresponding angles have a ratio of 2: 1
D. Their areas have a ratio of 4: 1
8. What is the value of π ?
A. π = 39
B. π = 54
C. π = 63
D. π = 90
9. In βπΏππ, π is the midpoint of πΏπΜ Μ Μ Μ , π is the midpoint of ππΜ Μ Μ Μ Μ , and R is the midpoint of πΏπΜ Μ Μ Μ . Given
the following, what is the perimeter of βπ ππ ?
πΏπ = 8.2π₯
ππ = 4.3π₯
ππ = 6π₯
A. 11.4π₯
B. 15.5π₯
C. 18.4π₯
D. 18.5π₯
11. Apply the dilation π·: (π₯, π¦) β (4π₯, 4π¦) to the triangle given below. Which of the
following is the perimeter of the image?
A. 41.9 π’πππ‘π
B. 40.5 π’πππ‘π
C. 20.5 π’πππ‘π
D. 9.2 π’πππ‘π
12. What is the length of π΄πΆΜ Μ Μ Μ ?
A. π΄πΆ = 28
B. π΄πΆ = 26
C. π΄πΆ = 24
D. π΄πΆ = 15
13.
In the diagram below π΅π·Μ Μ Μ Μ , π·πΉΜ Μ Μ Μ , and π΅πΉΜ Μ Μ Μ are midsegments and π΅πΆ = 10 and π΄πΈ = 12. Compare the
perimeters of βπΆπ·π΅ and βπ·πΈπΉ, then choose the statement below that is true.
A. The perimeter of βπΆπ·π΅ is greater.
B. The perimeter of βπ·πΈπΉ is greater.
C. A relationship cannot be determined.
D. The perimeters are the same.
14. Which method cannot be used in a coordinate proof to prove βπ΄π΅πΆ~βπ΄π·πΈ?
A. Use the Distance Formula to show π΄π΅
π΄π·=
π΄πΆ
π΄πΈ, and β π΄ β β π΄ by the Reflexive Property of
Congruence. (ππ΄π~)
B. Use the Distance Formula to show π΄π΅
π΄π·=
π΄πΆ
π΄πΈ=
π΅πΆ
π·πΈ . (πππ~)
C. Use the Reflexive Property of Congruence to show β π΄ β β π΄, then measure to show
β π΄π΅πΆ β β π·. (π΄π΄~)
D. Use the slope formula to show that the slope of π΅πΆΜ Μ Μ Μ and π·πΈΜ Μ Μ Μ are equal so π΅πΆΜ Μ Μ Μ β₯ π·πΈΜ Μ Μ Μ and
corresponding angles are congruent. (π΄π΄~)
16. The Hopewell people were Native Americans whose culture flourished in the central Ohio Valley
about 2000 years ago. The Hopewell people constructed earthworks using triangles, including
those below.
The diagram below shows the layout of some Hopewell earthworks. The centers of the Newark
Octagon, the Newark Square and the Great Circle were at the corners of the shaded triangle.
The three right triangles surrounding the shaded triangle form a rectangle measuring 12 units by
14 units. Which of the Hopewell triangles is similar to Triangle 1, Triangle 2, and Triangle 3 in