Download 4. )33)(33( − +

Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Do Now 10
Name:
Date:
Do Now 10 – Order of Operations Practice
Directions: Simplify each of the following expressions. Show your work; circle or box your
answer.
1.
5 4 − 6 − (−3) 2.
15(4 + 8)
2(2 + 1) − 1
3.
(8 − 4)2 + 8 ÷ 4 4.
(32 + 3)(32 − 3) Geo Week 4 Packet Page 1
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
Chapter 2 Quiz 1 Review
YOU MAY COMPLETE THIS ASSIGNMENT ON THIS SHEET.
Students will be able to (SWBAT):
•
•
•
•
•
•
Sketch figures and their intersections (TB 1.4)
Measure and add segments (TB 1.5)
Measure and classify angles. Add angle measures (TB 1.6)
Bisect a segment. Find the coordinates of the midpoint of a segment (TB 2.1)
Bisect an angle (TB 2.2)
Find measures of complementary and supplementary angles. (TB 2.3)
Content Review:
Geo Week 4 Packet Page 2
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
Geo Week 4 Packet Page 3
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
I.
Sketch figures and their intersections (TB 1.4)
Directions: Use the diagram at right to determine whether each statement is true or false.
1. Planes Q and R intersect at line n.
2. Planes P and Q intersect at line m.
3. Planes R and S do not appear to intersect.
4. Planes S and P do not appear to intersect.
5. Lines n and l appear to intersect.
6. Planes Q and S intersect at line m.
7. Lines l and m do not appear to intersect. II.
Measure and add segments (TB 1.5)
Directions: Measure each segment in centimeters. Round to the nearest tenth.
8.
9.
10.
Directions: Find the measure of each segment. All measurements are in centimeters.
11. Find AC (the length of
12. Find MN.
13. Find QR.
segment AC.)
Geo Week 4 Packet Page 4
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
III.
Measure and classify angles. Add angle measures (TB 1.6)
Directions: Find the measure of each angle.
14.
15.
16.
Directions: measure each angle. Round to the nearest degree.
17.
18.
19.
20.
Geo Week 4 Packet Page 5
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
IV.
Bisect a segment. Find the coordinates of the midpoint of a segment (TB 2.1)
Directions: Line ℓ𝓁 bisects the segment. Find the value of x. Show your work.
21.
22.
23.
24.
Directions: Sketch 𝐶𝐷 on the coordinate plane. Then use the midpoint formula to find the
coordinates of its midpoint.
25. C (2, 2), D (4, 8)
26. C (-5, 4), D (1, -2)
27. C (2, -3), D (3, -7)
Geo Week 4 Packet Page 6
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
V.
Bisect an angle (TB 2.2)
Directions: 𝐵𝐷 bisects ∠ ABC. Find the value of x.
28.
29.
VI.
30.
Find measures of complementary and supplementary angles. (TB 2.3)
Directions: Find the measure of a) the complement and b) the supplement of the angle. If none
exists, write N/A.
31. m∠A = 56°
32. m∠B = 89°
33. m∠C = 104°
34. m∠D = 160°
a.
a.
a.
a.
b.
b.
b.
b.
VII.
Open Ended Questions
Directions: for problems 35 through 38, show your work and/or explain how you got your
answer for each part of the problem. Answer sheets for theses problems are provided below.
35. Olivia drew two angles that were supplementary and adjacent (note: adjacent means sharing
a side and a vertex).
a. Draw and label a pair of angles that could be Olivia’s.
b. Curt drew two angles that were supplementary and non-adjacent. Draw a pair of
angles that could be Curt’s angles.
c. Isabelle thinks she can draw a pair of angles that are supplementary, but that could
not be Olivia’s pair or Curt’s Pair. Do you agree with Isabelle? Explain why or why
not.
Geo Week 4 Packet Page 7
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
36. Martin drew a line segment on the coordinate plane that had one endpoint at (-4, -2) and a
length of 10 units.
a. Graph the endpoint of Martin’s segment and draw a vertical line that has Martin’s
endpoint and a length of 10.
b. Draw a vertical line that had Martin’s endpoint and a length of 10.
c. Draw a non-vertical, non-horizontal segment that has Martin’s endpoint and a length
of 10. Show or explain how you got your answer.
d. Find the midpoint of the segment you drew in part c. Show or explain how you got
your answer.
37. Cam drew ∠GHJ, with a measure of 65°.
a. Make a to-scale drawing of Cam’s angle. Be sure to label all the points.
b. Cam then drew a second angle, ∠GHK, with a measure of 40°. Add ∠GHK to your
drawing. Be sure to include labels.
c. In a separate drawing, redraw ∠GHJ, and then add ∠GHK in a different place than in
part b. Be sure to include all labels.
38. Danny sketched the figure at right for a game of “Name That Intersection,” and then gave his
paper to Brady.
T
a. Brady named all the intersections of lines. Name
q
all of Brady’s intersections.
U
b. Prasuna took the figure next and named all the
J
R
l
p
K
intersections of planes. Name all of Prasuna’s
k
S
r
o
Q
intersections.
L
j
M
m
N
n
Geo Week 4 Packet Page 8
O
P
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
35.
36.
Geo Week 4 Packet Page 9
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 2 Quiz 1 Review
Name:
Date:
37.
38.
Geo Week 4 Packet Page 10
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Linear Vertical Pairs
Name:
Date:
Linear Pairs and Vertical Pairs – Notes and Investigations
Adjacent Angles
Definition:
Notation:
Figure:
Example:
Linear Pair of Angles
Definition:
Notation:
Figure:
Example:
Vertical Pair of Angles
Definition:
Notation:
Figure:
Example:
Geo Week 4 Packet Page 11
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Linear Vertical Pairs
Name:
Date:
Groupwork Investigation
Materials: a protractor, straight-edge
↔
Step 1 (Individually) Draw PQ and place a point R between P and Q. Choose another point S
→
↔
not on PQ and draw RS . You have just created a linear pair of angles. Place the “zero edge” of
↔
your protractor along PQ .
What do you notice about the sum of the measures of the linear pair of angles?
________________________________________________________________________
________________________________________________________________________
Step 2 Compare your results with those of your group. Does everyone make the same
observation? Complete the statement and copy it and the diagrams into your vocabulary
notebook.
Linear Pair Conjecture
If two angles form a linear pair, then _________________________________________.
If:
Then:
1
2
1
2
Geo Week 4 Packet Page 12
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Linear Vertical Pairs
Name:
Date:
Materials: a straightedge, patty paper
Step 1 Draw two intersecting lines onto patty paper or tracing paper. Label the angles as shown.
Which angles are vertical angles?
•
∠ ____ and ∠ _____ are vertical angles
•
∠ ____ and ∠ _____ are vertical angles
Step 2 Fold the paper so that the vertical angles lie over each other. What do you notice about
their measures?
Step 3 Fold the paper so that the other pair of vertical angles lie over each other. What do you
notice about their measures?
Step 4 Compare your results with the results of others. Complete the statement and copy it and
the diagrams into your vocabulary notebook.
Vertical Angles Conjecture
If two angles are vertical angles, then ___________________________________________.
If:
Then:
A
C
A
B
E
C
B
D
E
D
Geo Week 4 Packet Page 13
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Linear Vertical Pair
Name:
Date:
White Board Practice
Directions: Name the relationship: complementary, linear pair, vertical, or adjacent.
Geo Week 4 Packet Page 14
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Linear Vertical Pairs
Name:
Date:
Directions: Find the measure of angle b.
Geo Week 4 Packet Page 15
Geometry Level 2
Homework 14
Name:
Date:
Homework 14 – Vertical Angles and Linear Pairs
Directions: Use the figure at right to answer questions 1-4.
1. ∠1 and __?__ are a linear pair, and so are ∠1 and __?__.
2. ∠2 and __?__ are vertical angles.
3. If m∠3 = 150°, then m∠2 = __?__.
4. ∠4 = __?__.
Directions: Use the diagram to complete the statements. Be sure to include the name of the
angle in your answer.
5. m∠KPL = __?__" 6. m∠LPN = __?__"
7. m∠MPN = __?__" 8. m∠MPO __?__"
Directions: Find the value of the variable. Then use substitution to find m∠PQR.
9.
10.
11.
For question 12, show your work and/or explain how you got your answer for each part of the
problem.
Four intersecting lines that form eight angles can represent the flag of the United Kingdom. The
horizontal and vertical lines are angle bisectors, and the measure of ∠1 is 26.6". The angles that
appear to be right angles are right angles.
a. Draw the simplified diagram and mark all the congruent angles.
b. Find the measure of ∠2. Show or explain how you got your answer.
c. Find the measure of ∠4. Show or explain how you got your answer.
Geo Week 4 Packet Page 16