NAME
Module 1, HW 31
1. Given: SN // OW , SW // ON
Prove:
W
O
SNO  OWS
S
N
2. In the diagram below, under which transformation will ΔA′B′C′ be the image of ΔABC?
(1) rotation
(3) translation
(2) dilation
(4) glide reflection
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Module 1, HW 31
Geometry Common Core
3. Given: PC & HR bisect each other
Prove: ΔPEH  ΔCER
C
H
E
R
P
4. The coordinates of the vertices of parallelogram ABCD are A(−2,2), B(3,5), C(4,2), and
D(−1,−1). State the coordinates of the vertices of parallelogram A″B″C″D″ that result from
the transformation ry-axis.
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Module 1, HW 31
Geometry Common Core
̅̅̅ , ̅̅̅̅
̅̅̅ ≅ ̅̅̅̅
̅̅̅ ⊥ 𝐼𝑂
̅̅̅̅
5. Given: 𝑃𝐼
𝑂𝑁, 𝑃𝐼
𝑂𝑁 ⊥ 𝑃𝑁
Prove: ΔPIO  ΔONP
N
O
P
I
6. Which transformation can map the letter S onto itself?
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(1) glide reflection
(3) line reflection
(2) translation
(4) rotation
Module 1, HW 31
Geometry Common Core
̅̅̅̅ ≅ 𝑱𝑳
̅̅̅, 𝑱𝑲
̅̅̅̅ ∥ 𝑿𝒀
̅̅̅̅.
7. Given: 𝑱𝑲
̅̅̅̅ ≅ 𝑿𝑳
̅̅̅̅.
Prove: 𝑿𝒀
Hint: You will not need to prove the Δs congruent.
What type of Δ is ΔJKL?
8. Quadrilateral MNOP is a trapezoid with MN || OP. If M′N′O′P′ is the image of MNOP after a
reflection over the x-axis, which two sides of quadrilateral M′N′O′P′ are parallel?
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(1) M′N′ and O′P′
(3) P′M′ and O′P′
(2) M′N′ and N′O′
(4) P′M′ and N′O′
Module 1, HW 31
Geometry Common Core
̅̅̅̅̅,
̅̅̅̅̅ // 𝐸𝑈
̅̅̅̅, ̅̅̅̅̅
9. Given: 𝑀𝑂
𝑀𝑂  𝐸𝑈
S
E is the Midpoint of MS
Prove: ΔMEO  ΔESU
E
M
U
O
10. What is the image of the point (−5,2) under the translation T3,−4?
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(1) (−9,5)
(3) (−2,−2)
(2) (−8,6)
(4) (−15,−8)
Module 1, HW 31
Geometry Common Core
̅̅̅̅ , 𝐶𝐸
̅̅̅̅ ⊥ 𝐴𝐵
̅̅̅̅
̅̅̅̅ ⊥ 𝐴𝐶
11. Given: 𝐵𝐹
̅̅̅̅
̅̅̅̅
𝐴𝐸  𝐴𝐹
Prove: △ 𝐴𝐶𝐸 ≅ ∆𝐴𝐵𝐹.
12. In problem #11 above, what sequence of rigid motions will map ΔABF onto ΔACE?
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Module 1, HW 31
Geometry Common Core
13. In the diagram below, a square is graphed in the coordinate plane.
A reflection over which line does not carry the square onto itself?
(1) x =5
(3) y = x
(2) y =2
(4) x + y = 4
14. A sequence of transformations maps rectangle ABCD onto
rectangle A’B’C’D’, as shown in the diagram below.
Which sequence of transformations maps ABCD onto A’B’C’D’ and
then maps A’B’C’D’ onto A’’B’’C’’D’’?
(1) a reflection followed by a rotation
(2) a reflection followed by a translation
(3) a translation followed by a rotation
(4) a translation followed by a reflection
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Module 1, HW 31
Geometry Common Core
15. In the diagram below, ̅̅̅̅
𝐴𝐶 ≅ ̅̅̅̅
𝐷𝐹 and points A, C, D, and F are collinear on line ℓ.
Let ΔD’E’F’ be the image of ΔDEF after a translation along ℓ, such that point D is mapped
onto point A. Determine and state the location of F’. Explain your answer.
Let ΔD’’E’’F’’ be the image of ΔD’E’F’ after a reflection across line ℓ. Suppose that E’’ is
located at B. Is ΔDEF congruent to ΔABC? Explain your answer.
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Module 1, HW 31
Geometry Common Core