Download Chapter-04-Test

1 of 6
Advanced Geometry - Chapter 4 Test
Name:
1.
Period: ______ Date: ________
Identify each statement as true or false.
(1 pt each)
a. If two angles and a non-included side of one triangle are congruent to two angles and a
non-included side of another triangle, then the triangles are congruent.
__________
b. It is possible to construct a triangle with side lengths 12 cm, 15 cm, and 28 cm.
__________
c. The letters CPCTC are an abbreviation for the phrase “corresponding parts of
congruent triangles are congruent.”
__________
d. For ∆ABC, if mA = 52°, mB = 88°, and mC = 40°, then AB is the longest side.
__________
e. The altitude to the base of an isosceles triangle is also the median to the base.
__________
f. The altitude to the base of an isosceles triangle bisects the vertex angle.
__________
g. If the measure of an exterior angle of a triangle is 45°, then the sum of the measures of
the remote interior angles is 45°.
__________
h. The sum of the measures of the three angles of an acute triangle is less than the sum of
the measures of the three angles of an obtuse triangle.
__________
i. Side-Side-Angle is a congruence shortcut.
__________
j. Side-Angle-Angle is a congruent shortcut.
__________
k. The incenter of a triangle is equidistant from all three sides of the triangle. __________
l. The orthocenter of a triangle is the point of concurrency of the angle bisectors of the
three angles of the triangle.
__________
m. The centroid of a triangle always lies in the interior of a triangle.
__________
Advanced Geometry
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2.
Using the given information, complete the congruence statement and tell which congruence
shortcut supports the congruence statement. If the triangles cannot be shown to be
congruent from the information given, write “cannot be determined.”
(4 pts each)
a. SIK  
____
Which congruent shortcut: __________
b. JAR  
____
Which congruent shortcut: __________
c. TAL  
____
Which congruent shortcut: __________
d. KJT  
____
Which congruent shortcut: __________
e. TIK  
____
Which congruent shortcut: __________
f.
ITR  
____
Which congruent shortcut: __________
Advanced Geometry
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3.
4.
Find the measure of each lettered angle, givenp q . Also, state the reason (conjecture) or
computation on the right. (W)
(2 pts each)
(1)
a=
____
____________________________________
(2)
b = ________
____________________________________
(3)
c=
____
____________________________________
(4)
d=
____
(5)
e = ________
(6)
f=
____
(7)
g=
____
(8)
h = ________
Use a compass and a straightedge to construct an isosceles triangle with the segments given
below as sides. Show all your compass swings in construction.
(5 pts)
Advanced Geometry
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5.
Provide each missing reason or statement in this flowchart proof.
Given: CDB  CEA
CD  CE
(10 pts)
Prove: AE  BD
Here, you can figure out ∠𝐴 ≅ ∠𝐵 by Angle Sum Conjecture.
By Flowchart Proof:
6.
Write a proof of this statement – by paragraph proof. (W)
(5 pts)
Given: PR  PQ
PT  PS
Prove: PRT  PQS
Advanced Geometry
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7.
8.
∆ABC has vertices A(–1, 6), B(7, 4), and C(1, –2) and median AM . (W)
a.
Find the coordinates of M.
b.
Find the equation of AM .
The function rule f(n) generates the sequence: –22, –14, –6, 2, 
(3 pts each)
(3 pts each)
a. Find the nth term (general rule).
b. Find the 20th term.
9.
Arrange a, b, c, d, and e in order from greatest to least.
(5 pts)
e
34°
a
b
d
43°
43°
38°
c
Answer:
_____ > _____ > ____ > ____ > _____
Advanced Geometry
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10.
If two sides of a triangle measure 5cm and 8cm, what is the range of length for the third
side? (W)
(5 pts)
11.
Given the figure below, find the value of x. (W)
(5 pts)
4x-5
7x+2
129°
Bonus Question:
12. Given the perimeter of ∆𝑇𝑂𝐸 is 605cm, find TE and 𝑚∠𝑇. (W)
(5 pts)
E
x
285cm
x + 99°
O
160cm
T
TE = _______________
𝑚∠𝑇 = _____________
Advanced Geometry