Test: Unit 2b/2c Retake

Test: Unit 2b/2c Retake
Extra Problems
Each boxed section represents a portion of the test that can be retaken. Your new grade will be computed based on the
better of the grades within each section.
OBJ: You will be able to discover and use shortcuts for showing that two triangles are congruent (Q1-Q4)
On Q1-Q4, determine which triangles, if any, are congruent. State the congruence conjecture that supports the
congruence statement. If the triangles cannot be shown to be congruent from the given information, write “Cannot
be determined.”
1.
HIJ  _________ by __________
2.
STP  _________ by __________
3.
ADB  _________ by __________
4.
KJT  _________ by __________
If you missed any of the above questions, complete a-d below.
a) ∆𝑀𝑂𝑁 ≅ ∆______ by ______
b) ∆𝑆𝑄𝑅 ≅ ∆______ by ______
c)
∆𝐴𝐵𝐶 ≅ ∆______ by ______
d) ∆𝑀𝑃𝐷 ≅ ∆______ by ______
OBJ: You will be able to find the measures of the interior and exterior angles of a triangle (Q5-Q8)
5.
What property of triangles does the picture below
illustrate?
A
a) Prove the Triangle Exterior Angle Theorem
b) Prove that a set of exterior angles of a triangle
sum to 360 (𝑚∠1 + 𝑚∠2 + 𝑚∠3 = 360°)
1
A
B
C
B
E
3
2
6.
What is the value of x in radians?
a)
What is the value of x in radians?
7π
9
2π
x
7
x
b) What is the value of x and y in radians?
x
π
4π
12
15
y
7.
Find the value of c.
Find the value of 𝑐.
a)
80
80
c
c
a
b
a
b
a
b
b
a
b) Find the value of z.
C
y
x
z
43°
y
x
A
B
8.
Find the values of x and y.
𝑥=
𝑦=
a)
Find the values of 𝑥 and 𝑦.
b) Find the measures of each lettered angle.
OBJ: You will be able to discover, use, and prove various theorems about perpendicular bisectors and angle bisectors
(Q9, Q10, Q17)
OBJ: You will be able to discover, use, and prove various theorems about points of concurrency (Q11-Q16)
9.
Find the values of x and y.
x=
y=
a) Find the values of x and y.
b) Find the values of x and y.
10. What is mCAB?
11. Point Z is the circumcenter of WXY. What is
ZY?
Purple Geometry Textbook:
a) P. 313: 13
b) P. 313: 14
a)
Purple Geometry Textbook P. 307: 16
b) Purple Geometry Textbook P. 307: 17
12. Point S is the centroid of PQR. If QS = 3x + 5
and QT = 4x + 11, find the value of x.
x=
a)
Geometry Textbook P. 323: 33
b) Geometry Textbook P. 323: 34
13. Archeologists find three stones that they
believe were once part of a circle of stones with
a community firepit at its center. Given the
diagram below, how could the archeologists
find the location of the firepit?
a)
Purple Geometry Textbook P. 308: 25
b) Purple Geometry Textbook P. 315: 29
Stone 1
Stone 2
Stone 3
A. They could find the incenter of the triangle
formed by the three stones.
B. They could find the orthocenter of the
triangle formed by the three stones.
C. They could find the circumcenter of the
triangle formed by the three stones.
D. They could find the centroid of the triangle
formed by the three stones.
14. Given the inscribed circle with center K, which
statement can you NOT conclude?
a)
Purple Geometry Textbook P. 314: 23
b) Purple Geometry Textbook P. 317: 3
A.
B.
C.
D.
XK = YK
̅̅̅̅̅
𝑁𝐾 ⊥ ̅̅̅̅
𝑌𝑍
∠𝑁𝑍𝐾 ≅ ∠𝑂𝑍𝐾
MK = OK
15. Find the value of x that makes P the incenter of
WST.
a) Geometry Textbook P. 314: 25
b) Find the value of 𝑥 that makes 𝐽 the incenter of
the triangle.
16. ABC sits comfortably in the coordinate plane
below. Find the approximate location of its
orthocenter.
ABC sits comfortably in the coordinate planes below. Find
the approximate location of each orthocenter.
a)
B
C
6
6
4
4
2
B
2
5
5
2
-2
A
A
4
C
6
b)
8
B
6
4
A
2
C
5
17. Complete each statement as fully as possible.
a) L is equidistant from
____________________
a)
Complete each statement as fully as possible.
a) M is equidistant to: __________
b) P is equidistant to: __________
10
b) M is equidistant from
___________________
c)
c) Q is equidistant to: __________
d) R is equidistant to: __________
N is equidistant from
___________________
d) O is equidistant from
___________________
b) Complete each statement as fully as possible.
a) J is equidistant to: __________
b) K is equidistant to: __________
c) I is equidistant to: __________
B
G
C
J
I
F
K
H
E
D
OBJ: You will be able to discover, use, and prove the Midsegment Theorem (Q18)
OBJ: You will be able to complete and use the Triangle Inequality Theorems (Q19-Q23)
OBJ: You will be able to write a coordinate proof (Q24, Q25)
̅̅̅̅, 𝑅𝑇
̅̅̅̅ , 𝑆𝑇
̅̅̅̅, ̅̅̅̅̅
̅̅̅̅ are all
18. If 𝑅𝑆
𝑊𝑌 , ̅̅̅̅̅
𝑊𝑍, and 𝑌𝑍
midsegments, find x.
x=
a) Purple Geometry Textbook P. 300: 39
b) Purple Geometry Textbook P. 301: 43
19. Two sides of an isosceles triangle are 3 inches and 7
inches. What is the perimeter of the triangle?
a)
Two sides of an isosceles triangle are 14 meters
and 6 meters. What is the perimeter of the
triangle?
b) The perimeter of HGF must be between what
two integers?
20. Determine if the following measures could be used
as the lengths of the sides of a triangle.
A. 4 cm, 6 cm, 9 cm
B. 4 in, 6 in, 10 in
C. 4 m, 6 m, 11 m
D. All of the above
21. If the lengths of two sides of a triangle are 7 m and
8 m, which graph shows the possible value of the
third side of the triangle?
A.
B.
C.
D.
7
8
7
8
1
a)
If the lengths of two sides of a triangle are 6 m
and 12 m, draw a graph showing the possible
value of the third side of the triangle.
b) If the lengths of two sides of a triangle are 1234
miles and 4567 miles, draw a graph showing the
possible value of the third side of the triangle.
15
7
Determine if the following measures could be used as the
lengths of the sides of a triangle:
a) 1 unit, 1 unit, 1 unit
b) 1 unit, .5 unit, .5 unit
c) 1 unit, .25 unit, .75 unit
d) 1 unit, .75 unit, .75 unit
15
22. List the sides of the triangle in order from least to
greatest.
a)
Purple Geometry Textbook P. 331: 10
b) Purple Geometry Textbook P. 331: 11
D
37
76
E
F
A.
B.
C.
D.
̅̅̅̅
𝐷𝐸 , ̅̅̅̅
𝐸𝐹 , ̅̅̅̅
𝐹𝐷
̅̅̅̅
̅̅̅̅
𝐹𝐷, 𝐸𝐹 , ̅̅̅̅
𝐷𝐸
̅̅̅̅
𝐸𝐹 , ̅̅̅̅
𝐷𝐸 , ̅̅̅̅
𝐹𝐷
̅̅̅̅
𝐹𝐷, ̅̅̅̅
𝐷𝐸 , ̅̅̅̅
𝐸𝐹
23. Find the possible values of x.
a) Use the Triangle Inequality Theorem to find
all possible values of x. Write your answer as
a compound inequality.
b)
24. Place an isosceles triangle in the coordinate plane
in such a way that it is convenient for finding side
lengths. Assign variables for the coordinates of
each vertex.
y
x
Use the Triangle Inequality Theorem to find
all possible values of x. Write your answer as
a compound inequality.
a) Purple Geometry Textbook P. 298: 2
b) Purple Geometry Textbook P. 298: 16
25. Referring to Q24, write a coordinate proof to show
that the two medians connecting the base angles to
the legs are congruent.
a) Purple Geometry Textbook P. 300: 36
b) A kite can be drawn in the coordinate plane as
shown below. Write a coordinate proof to show
that the diagonals of a kite are perpendicular.
y
I (0, c)
K
T
( a, 0)
(b, 0)
E (0, c)
x