Name______________________________
Period ______
February Break
Part 1 – In this section no work needs to be shown.
Place all answers on answer sheet. [2]
6. Which statement is sufficient evidence that
is congruent to
?
1. The diagonals of a square intersect at the origin.
Which transformation would not map the square
onto itself?
(1) 𝑟𝑦−𝑎𝑥𝑖𝑠
(2) 𝑅−270
(3) 𝑇3,−3 (4) 𝑟𝑦=−𝑥
2. In the diagram below, congruent figures 1, 2, and 3
are drawn. Which sequence of transformations
maps figure 1 onto figure 2 and then figure 2 onto
figure 3?
(1)
and
(2)
,
,
(3) There is a sequence of rigid motions that maps
onto
,
onto
, and
onto
.
(4) There is a sequence of rigid motions that maps
point A onto point D,
onto
.
(1)
(2)
(3)
(4)
(1) diagonals are perpendicular
(2) diagonals are congruent
3. Quadrilateral ABCD has diagonals
and
.
Which information is not sufficient to prove ABCD is
a parallelogram?
(1) ̅̅̅̅
𝐴𝐶 and ̅̅̅̅
𝐵𝐷 bisect each other.
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ and 𝐵𝐶
̅̅̅̅ ≅ 𝐴𝐷
̅̅̅̅
(2) 𝐴𝐵
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ and 𝐴𝐵
̅̅̅̅ ∥ 𝐶𝐷
̅̅̅̅
(3) 𝐴𝐵
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ and 𝐵𝐶
̅̅̅̅ ∥ 𝐴𝐷
̅̅̅̅
(4) 𝐴𝐵
,
6,
statement is true?
(1) <CAB ≅<DEF
(2)
𝐴𝐵
𝐶𝐵
=
𝐹𝐸
𝐷𝐸
, and
, and
7. A parallelogram must be a rectangle when its
a reflection followed by a translation
a rotation followed by a translation
a translation followed by a reflection
a translation followed by a rotation
4. Triangles ABC and DEF are drawn below. If
onto
,
, which
(3) opposite sides are parallel
(4) opposite sides are congruent
Part 2 – In this section to receive any credit work
must be shown in space provided. Choose the best
answer on the answer sheet. [5]
8. In the diagram of
, and
the nearest tenth?
below,
,
,
̅̅̅̅ , to
. What is the length of 𝐵𝐶
(3) ∆𝐴𝐵𝐶 ~∆𝐷𝐸𝐹
(4)
𝐴𝐵
𝐷𝐸
𝐹𝐸
= 𝐶𝐵
5. Steve drew line segments ABCD, EFG, BF, and CF as
shown in the diagram below. Scalene
is
formed. Which statement will allow Steve to prove
(1) 5.1
(2) 5.2
(3) 14.3
(4) 14.4
9. In the diagram below,
,
, and the perimeter of
what is the perimeter of
?
. If
,
is 30,
?
(1) < CFG ≅ < FCB
(2) < ABF ≅ < BFC
(3) < EFB ≅ < CFB
(4) < CBF ≅ < GFC
(1) 12.5
(2) 14.0
(3) 14.8
(4) 17.5
10. In the diagram of parallelogram FRED shown below,
is extended to A, and
. If
14. In the diagram below of right triangle ABC, altitude
is drawn such that
, what is
is drawn to hypotenuse
?
what is the length of altitude
(2) 6√5
(1) 6
(1) 124𝑜
(2) 112𝑜
(3) 68𝑜
11. In the diagram below, transversal
and
(4) 56𝑜
In
,
?
(3) 3
(2) 16
12. In the diagram of
extended to S,
(3) 24
shown below,
,
, and
. What is
, and
. What is
(2) 35
(3) 60
is
?
(2) 6
(3) 3
(4) 4
17. As shown in the diagram of rectangle ABCD below,
diagonals
and
intersect at E. If
, then the length of
(2) 40
(3) 11
,M
is the midpoint of
, and N is the midpoint of
,
, and
, the perimeter of
trapezoid BMNC is
. If
(3) 28
and
is
(4) 10
shown below, L is the midpoint of
(2) 31
(4) 90
(4) 28
17.
(1) 35
,
16. The measure of an interior angle of a regular
polygon is 120°. How many sides does the polygon
have?
(1) 5
13. In
(4) 3√5
?
16.
(1) 44
,
m < D?
(1) 25
(1) 6
and
15. In the diagram of trapezoid ABCD below,
intersects
at V and W, respectively. If
and
, for which
value of x is
. If
(1) 6
(2) 10
(3) 12
(4) 24
̅̅̅̅ is the altitude drawn to
18. In the diagram below, 𝐶𝐷
̅̅̅̅ of right triangle ABC. Which lengths
the hypotenuse 𝐴𝐵
would not produce an altitude that measures 6√2 ?
(4) 26
(1) AD = 2 and DB = 36
(3) AD = 6 and DB = 12
(2) AD = 3 and AB = 24
(4) AD = 8 and DB = 17
NAME______________________________ Pd ___
ANSWER KEY
Part 3 – In this section to receive any credit work
must be shown in space provided. Place your
answer on the answer sheet. [7]
1 _____________________
19. In ∆𝐴𝐵𝐶, ̅̅̅̅
𝐴𝐷 bisects < CAB. AB = 12, BC = 20,
AC = 8. Find x and y.
2_____________________
3_____________________
1
4_____________________
5_____________________
20. Simplify:
3
2_
6_____________________
1
7_____________________
7−√2
8_____________________
2_
9_____________________
1
10_____________________
11_____________________
2_
12_____________________
13 _____________________
14_____________________
15_____________________
16_____________________
17_____________________
18_____________________
19_____________________
20_____________________
Part 4 – In this section you must use a compass and Pa
straight edge. [6]
Part 5 – In this section to receive credit prove the
following. [10]
21. Triangle XYZ is shown below. Using a compass and
straightedge, on the line below, construct and label
∆ABC, such that ∆ABC is congruent to ∆XYZ. [Leave all
construction marks.]
̅̅̅̅̅ and 𝐷𝐸
̅̅̅̅
23. Given: Parallelogram ANDR with 𝐴𝑊
̅̅̅̅̅̅
̅̅̅̅̅̅̅
bisecting 𝑁𝑊𝐷 and 𝑅𝐸𝐴 at points W and E respectively.
Based on your construction, state the theorem that
justifies why ∆ABC is congruent to ∆XYZ.
Prove that ∆𝐴𝑁𝑊 ≅ ∆𝐷𝑅𝐸
Prove that quadrilateral AWDE is a parallelogram
A
N
E
W
R
22. Using a compass and straightedge, construct an
equilateral triangle with
as a side. Using this
triangle, construct a 30° angle with its vertex at A.
[Leave all construction marks.]
D