Download Chapter 10 Test Corrections

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Question 1
In this problem, you just needed to check your notes, if
you had them with you. If not, you really should’ve known
which of these were supplementary, because the rest
were congruent.
These are all
congruent
angles.
These are
supplementary
angles.
Question 2
AIA’s
AEA’s
Oh, wait, 2 and 8 were a pair in there?
Question 3
What angles are in the same position?
Top Right
Top Left
Bottom Right
Top Right
Top Left
Bottom Left
The same position! Top Right!
Question 4
The easiest thing to do is actually put 49 degrees
into the angle.
Angle 6 is vertical with angle 8, so they’re congruent.
131ᵒ
49ᵒ
49ᵒ
131ᵒ
131ᵒ
49ᵒ
49ᵒ
131ᵒ
180-49=
Angle 2 is corresponding with angle 6, so they’re congruent.
Angle 4 is vertical with angle 4, so they’re congruent.
Angle 7 is linear with angle 8, so they’re supplementary.
Angle 5 is vertical with angle 7, so they’re congruent.
Angle 1 is corresponding with angle 5, so they’re congruent.
Angle 3 is vertical with angle 1, so they’re congruent.
Question 5
13+26= 39°
3(3) = 39°
What kinds of angles are these?
(vertical angles)
So are they congruent or supplementary?
(congruent)
Since they’re congruent, make both angles
equal to each other:
3𝑥 = 𝑥 + 26
-x -x
2𝑥 = 26
2
2
𝑥 = 13
subtract x from both sides to move it all to one side
divide by 2 to get x by itself
Question 6
x = 30°
5(30) = 150°
What kinds of angles are these?
(linear angles)
So are they congruent or supplementary?
(supplementary)
Since they’re supplementary, they add up to
180: 𝑥 + 5𝑥 = 180
6𝑥 = 180
6
6
𝑥 = 30
combine your x’s (your “like” terms)
divide by 6 to get x by itself
Question 7
45˚+45˚≠180˚
50˚+50˚≠180˚
90˚+90˚=180˚
This means 2 CONGRUENT angles. This means they also add up to 180˚.
(They have the same measure.)
Question 8
This means 2 CONGRUENT angles.
(Their measures will be equal.)
m<1=m<2
2𝑥 + 11 = 5𝑥 − 25
−2𝑥
−2𝑥
11 = 3𝑥 − 25
But before you go getting all
+25
+25
circle happy and thinking it’s A…
36 = 3𝑥
3
3
𝒎 < 𝟐 = 𝟓𝒙 − 𝟐𝟓
12 = 𝑥
𝒎 < 𝟐 = 𝟓 𝟏𝟐 − 𝟐𝟓
𝒎 < 𝟐 = 𝟔𝟎 − 𝟐𝟓
𝒎 < 𝟐 = 𝟑𝟓˚
They want the actual angle
measure, not what x is.
move all the x’s to one side by subtraction
Question 9
If this angle is 57°…
Then this angle must also be 57°
(because the two angles are AEA’s)
…and that angle is 90° (see the right angle marking?)…
And if that angle *is* 57°…
Then this angle is 33°.
And that angle is
supplementary with x, so
33+x=180....
x =147
180-57-90=33
…and all
together, they
form a triangle,
which has a
total of 180°…
Question 10
First of all…
…your answer will be one of these.
Again, not quite what we need.
2
−𝑦 = 12 − 𝑥
5
All we need to do to get this equation into y=mx+b
form is change the sign of y. But what we do to one
side of the equation, we do to everything on the
other side of the equation.
2
𝑦 = −12 + 𝑥
5 𝒔𝒍𝒐𝒑𝒆 = 𝟐
𝟓
Not quite in y=mx+b form, but we can get there!
2𝑦 = −5𝑥 − 9
2
2
2
divide everything by 2 to get y by itself
−5
9
𝑦= 2 𝑥−2
don’t reduce – slope is best left as a fraction!
−𝟓
𝒔𝒍𝒐𝒑𝒆 =
𝟐
These slopes are negative
reciprocals, so the lines are
perpendicular.
Question 11
First of all…
…your answer will be one of these.
Again, not quite what we need.
−2𝑦 = −6𝑥 + 5
-2
-2 -2 divide by -2 to get y by itself
5
𝑦 = 3𝑥 −
2 𝒔𝒍𝒐𝒑𝒆 = 𝟑
Not quite in y=mx+b form, but we can get there!
3𝑦 = 𝑥 − 12
3
3
3
divide everything by 3 to get y by itself
1
𝑥
1𝑥
𝑦 = 3𝑥 − 4
do remember that x is the same as 1x so =
3
3
𝟏
𝒔𝒍𝒐𝒑𝒆 =
𝟑
These slopes are reciprocals, but not negative reciprocals,
so the lines are just
neither.
Question 12
X
+5
Y
X
How do you find the slope of
two coordinates?
𝚫𝒚
𝚫𝒙
Y
+5
or
𝒚𝟐 −𝒚𝟏
𝒙𝟐 −𝒙𝟏
𝒚𝟐 − 𝒚𝟏
−6 − 4
−6 − 4 −10
=
=
=
= −2
𝒙𝟐 − 𝒙𝟏 3 − (−2)
3+2
5
(add 5 to your x coordinates)
C’ (8, -6) D’ (3, 4)
You could calculate this or remember what you learned about slopes after translating.
𝒚𝟐 − 𝒚𝟏 −6 − 4 −10
=
=
= −2
𝒙𝟐 − 𝒙𝟏
8−3
5
The lines are parallel, because the slopes are the same.
If you made a simple mistake with your math, like thinking
3 – (-2) = -5 or 1 or -1, perhaps one of your best strategies for
next time is to borrow a calculator.
If you mixed up which is x and which is y, keep making a
note of it on your notes, worksheets, etc.
Question 14
This is the only option that we
know for sure. Because the
triangles have the same
shape, and proportional sides,
they’re similar. If they’d had
lengths, we might have had a
chance at choosing c or d.
Are they congruent? The same size? nope.com
Are they similar? They’re the same shape, not the same size… so maybe.
Well… they could be. But there’s
nothing to tell us they are FOR SURE.
So we’ll have to say no.
And like option C, without measurements, there’s nothing to tell us this FOR SURE.
Question 15
X, Y
P
X, Y
X, Y
X, Y
If you noticed the
slopes were the
same, you
might’ve marked
parallel lines.
Q
R
S
However, if you
borrowed a scratch
paper to graph the
two lines, they’re
actually like… the
same line (otherwise
known as…
COINCIDENTAL
LINES)!!!
To figure out how the lines are related,
we’ll have to find their slopes.
−5
10
=
−1
2
slope of QS: 𝒙𝟐−𝒙𝟏 = 10−(−2) = 10+2 =
−6
12
=
slope of PR:
𝒚𝟐 −𝒚𝟏
𝒙𝟐 −𝒙𝟏
𝒚 −𝒚
𝟐
𝟏
=
4−9
4−(−6)
1−7
=
4−9
4+6
=
1−7
The slopes of PR and QS are the same!
−1
2
Question 16
If this angle is 65°…
If this angle is 70°…
70°
45°
70°
65°
65°
65° 115°
70°
Let’s do the same
for our 45° angles.
45°
65°
65° 45° 70°
65° 45° 70°
If this angle is 70°…
115°
…then so are these.
If this angle is 65°…
45°
65°
65° 45° 70°
180-65=115
…then so are these.
…then so are these.
70°
110°
110°
70°
That really only leaves a few angles.
…then so are these.
180-70=110
BOOM!!!
DONE.
Remember that these angles are linear pairs with the
angles they touch, which means they add up to 180°.
Admittedly, there was a lot
here. If you notice from the
point value, you needed to find
23 angles.
Start by labeling the angles you
do know.
Then, label their vertical angles.
Remember, vertical angles are
congruent.
It comes down to
corresponding angles after that
(angles that are in the same
position). Because of all the
parallel lines, we know our
corresponding angles are
congruent.
Please turn your corrected test in to your
teacher and continue on to the next
activity.