M218—Honors Geometry
Chapter 1—Introduction to Geometry
Answers for Test Review HW
Name: _________________
Teacher: _______________
−8 + 2
= −3
2
b) 2 − x = 15
17 ) a)
− 13 = x
2
.
5
b) The first time you pick, you have a 2 out of 5 chance of getting a midpoint.
Assuming you picked a midpoint the first time, then there is one midpoint left out of 4
remaining points. To get our probability, we multiply both of these probabilities
together:
19) a) There are 2 midpoints out of 5 points total in the diagram, so P =
2 1
2
1
• =
=
5 4 20 10
20) Since we are trisecting a 40.2 degree angle, to find the measure of one of the
three angles formed, we divide 40.2 degrees by 3:
40.2°
= 13.4° or 13°24'
3
21) c)
4(30° ) +
15
(30° ) = 127.5°
60
30°
30°
30°
30°
25) 3x + 2x = 25
5x = 25
x = 5
So WX = 3x = 3(5) = 15
15
(30°)
60
3x
W
2x
X
Y
27)
Statements
(1) ∠ABC is a rt angle
Reasons
(1) Givens
∠DBC = 20°, ∠FEG = 40°, ∠GEH = 30°
(2) m∠ABC = 90°
(2) If an ∠ is a rt ∠, then its measure is 90°
(3) m∠HEF = 70°
(3) Addition (40° + 30° = 70° )
(4) m∠ABD = 70°
(4) Subtraction (90° − 20° = 70° )
(5) ∠ABD ≅ ∠FEH
(5) If two angles have the same measure, then
they are ≅
29) m∠1 = 180° − 60°29 '− 70°40 '16 " = 48°50 ' 44 "
33)
19 − 12 < PR < 19 + 12
7 < PR < 31
34) First, we set up a system of equations. We know both angles sum to 25, and that
they are congruent. These two observations yield two equations:
⎧ (2x − y) + (3y − x) = 25
⎨
⎩2x − y = 3y − x
Now start the solving process by getting each equation in standard form (x’s and y’ on
the left, numbers on the right):
⎧ x + 2y = 25
⎨
⎩3x − 4 y = 0
Multiply the first equation by 2:
⎧2(x + 2 y = 25)
⎧2x + 4 y = 50
, so we get ⎨
⎨
⎩3x − 4 y = 0
⎩3x − 4 y = 0
Add the two equations together:
5 x = 50 , so x = 10.
Plug back into 3x − 4 y = 0 to get y:
3(10) − 4 y = 0
−4 y = −30
y =
15
2
35) a) 90 < m∠Q < 180
b)
90 < 2x − 28 < 180
118 < 2x < 208
59 < x < 104
36)
x2 − 27 x = 90
x2 − 27 x − 90 = 0
(x − 30 )(x + 3) = 0
x = 30 or x = −3
Notice—both solutions are kept in this case! You don’t have to throw away x = -3 just
because it’s negative! When you substitute either of these into the original expression,
they both work.