Honors Geometry
Chapter 1 Review
True/False
1.
_____ AD ≅ DE ≅ EC
2.
_____m∠DBE = 30°
3.
_____m∠ABE = 2(m ∠EBC)
C
B
E
D
A
Always/Sometimes/Never
4.
_____A line has a bisector.
5.
_____A false statement has a false converse.
6.
_____An angle whose measure is between 0° and 90° is an acute angle.
7.
_____The sum of two acute angles is an acute angle.
Fill in the blanks.
8.
uuur
uuur
_____ AD ∩ EA
9.
uuur
uuur
_____DA ∪ DB
10.
suur
suur
_____ AD ∩ BC
11.
_____∠ABE ∩ ∠EBC
12.
_____The number of angles that have their vertex at point B.
13.
_____If three of the five labeled points are chosen at random, what is the probability that they
form a triangle?
Use the following logical sentences for both parts of question 14.
14.
You are an honors geometry student and therefore you want to get an A on this test. If you
don’t know the material in Chapter 1, you won’t get an A on this test.
a.) Write the first sentence in if ⇒ then form.
b.) What can you conclude?
15.
Write the sentence in if ⇒ then form.
All obtuse triangles have exactly one obtuse angle and two acute angles.
16.
Write the converse of this statement.
If a number is divisible by six, then it is divisible by three.
17.
Find the angle between the hands of a clock at 11:35.
12
11
1
2
10
3
9
4
8
5
7
18.
Change 33’20’’ to degrees.
19.
∠ABC is a right angle. Find m∠ABD.
6
A
D
B
20.
∠2 is five times as large as ∠1. Find m∠2.
10° 35' 10''
C
2
1
21.
P
uuur
QS bisects ∠PQR. Solve for y in terms of x.
Q
S
(5 x-6) °
(x-2y)°
R
22.
If ST = 4, SE = 11, ET = 7, and S, T, and E are collinear, then point _____ is between the
other two points. Justify your answer with a diagram.
23.
The sides of a triangle are in the ratio 4:5:7 and the perimeter of the triangle is 72. Find the
length of the shortest side.
24.
Given: EB and EC trisect AD
AB = 7x+3
AC = 11y-7
CD = 8x+2y-10
A
Find:
B
E
AD
C
D
25.
In the figure, is ∠QPS ACUTE, RIGHT, or OBTUSE? Write a paragraph proof to justify your
answer. P
(2 x+10) °
(x+25)°
(3 x)°
Q
(5 x-20) °
R
S
26.
A triangle has sides 3 cm and 11 cm. What are the restrictions on the length of the third side?
27.
Subtract. 90° - 30° 52’ 20’’.
28.
Given: m ∠AXB = 70°
m ∠BXY = 20°
∠Y is a right angle
A
B
Prove: ∠AXY ≅ ∠Y
X
Y
Honors Geometry
Chapter 1 Review – Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
False
False
True
Never
Sometimes
Always
Sometimes
EA
∠BDA
C
11.
12.
BE
6
3
5
a.)
b.)
13.
14.
If you are an honors geometry student, then you want to get an A on the test.
If you are an honors geometry student, then you know the material.
OR
If you don’t know the material, then you are not an honors geometry student.
15.
If a triangle is an obtuse triangle, then it has exactly one obtuse angle and two acute angles.
16.
If a number is divisible by three, then it is divisible by six.
17.
137.5° or 137°30’
18.
5
°
9
19.
79° 24’ 50’’
28.
20.
150°
Statements
Reasons
21.
y = -2x + 3 or y = 3 – 2x
1. given
22.
T
1. m ∠AXB = 70°
m ∠BXY = 20°
∠Y is a right angle
23.
18 units
2. m ∠AXY = 90°
2. addition
24.
x = 3, y = 5, AD = 72
3. m ∠Y = 90°
3. right ∠ = 90°
25.
∠QPS is obtuse (m ∠QPS = 110°)
4. ∠AXY ≅ ∠Y
4. 2 ∠s with =
measures are ≅
26.
8 < x < 14
27.
59° 7’ 40’’