ACTIVITY 12 Continued
Lesson 12-2
More Geometric Figures
ACTIVITY 12
Lesson 12-2
continued
PLAN
My Notes
Learning Targets:
• Describe angles and angle pairs.
• Identify and name parts of circles.
Pacing: 1 class period
Chunking the Lesson
#1–4
#5–7
Check Your Understanding
Lesson Practice
SUGGESTED LEARNING STRATEGIES: Think-Pair-Share, Self
Revision/Peer Revision, Discussion Groups, Create Representations
As you share your ideas, be sure to use mathematical terms and academic
vocabulary precisely. Make notes to help you remember the meaning of new
words and how they are used to describe mathematical ideas.
TEACH
Bell-Ringer Activity
1. Draw four angles with different characteristics. Describe each angle.
Name the angles using numbers and letters. Students should draw
On the board, draw a diagram of a KWL
Chart and have students copy it. List
terms that students will encounter in
this lesson and have students write those
terms in their own KWL Charts. Terms
should include acute angle, right angle,
obtuse angle, straight angle,
complementary angles, supplementary
angles, adjacent angles, vertical angles,
diameter, radius, chord, and concentric
circles. Suggest that students revise this
chart as they work through the lesson
until all terms are in the Know or
Learned columns.
and label one acute angle, one obtuse angle, one right angle, and
one straight angle. Sample angles:
A
1
B
X
2
C
Y
Z
D
4
3
E
F
Q
R
P
2. Compare and contrast each pair of angles. Sample answers given.
a.
b.
© 2017 College Board. All rights reserved.
© 2017 College Board. All rights reserved.
1
2
D
∠1 and ∠2 are
supplementary and
adjacent; ∠1 is acute
while ∠2 is obtuse.
c.
When you compare and contrast
two figures, you describe how they
are alike or different.
B
C
∠ADB and ∠BDC are
complementary and
adjacent.
R
D
60°
30°
E
A
ACADEMIC VOCABULARY
F
S
T
∠DEF and ∠RST are complementary. They are not adjacent.
d.
D
E
150°
X
30°
F
Y
1–4 Activating Prior Knowledge,
Think-Pair-Share, Self Revision/
Peer Revision, Discussion Groups,
Create Representations Ask students
whether it is possible for two angles to
be both complementary and
supplementary, or if it is possible for an
angle to be the complement of one angle
and the supplement of another angle. If
so, ask them to describe such an angle.
They should conclude that no two
angles can be complementary and
supplementary, but that an angle may be
the complement of one angle and the
supplement of another if the angle is
acute. Challenge students to illustrate
their conclusions with diagrams.
Z
∠DEF and ∠XYZ are supplementary. They are not adjacent.
Activity 12 • Geometric Figures
215
Activity 12 • Geometric Figures
215
ACTIVITY 12 Continued
My Notes
3. a. The figure below shows two intersecting lines. Name two angles that
are supplementary to ∠4. ∠3 and ∠5
Remind students that adjacent angles
have a common vertex and a common
side between them. Challenge students
to draw two angles with a common
vertex that are not adjacent, two angles
with a common vertex and a common
side that are not adjacent, and two
angles with a common vertex and a
common side between them. Emphasize
that the common side must be inside the
angle formed by the two rays that the
angles do not have in common.
As you guide students through their
learning of these new essential
mathematical terms, explain meanings
in terms that are accessible for your
students. As much as possible, provide
concrete examples to help students gain
understanding. Encourage students to
make notes about new terms and their
understanding of what they mean, and
how to use them to describe precise
mathematical concepts and processes.
The sum of the measures of complementary angles is 90°, and the sum of the
measures of supplementary angles is 180°.
b. Reason quantitatively. Explain why the angles you named in part
a must have the same measure.
3
6
Sample answers: ∠3 is supplementary to ∠4, so the sum of their
measures is 180°. ∠5 is supplementary to ∠4, so the sum of their
measures is 180°. So ∠3 and ∠5 must have the same measure.
MATH TIP
4. Complete the chart by naming all the listed angle types in each figure.
Angles can be classified by their
measures.
C
• An acute angle measures greater
than 0° and less than 90°.
• A right angle measures 90°.
• An obtuse angle measures greater
than 90° and less than 180°.
• A straight angle measures 180°.
8 7
10 9
216
A
D
B
E
F
Acute angles
∠8, ∠9
∠ABF; ∠CBD; ∠EBD
Obtuse angles
∠7, ∠10
∠FBC; ∠ABD; ∠EBF
∠8 and ∠9
∠7 and ∠10
∠ABF and ∠EBD;
∠ABC and ∠CBE;
∠ABD and ∠FBE;
∠ABE and ∠FBD
Supplementary
angles
∠8 and ∠7; ∠8 and ∠10;
∠7 and ∠9; ∠9 and ∠10
∠ABF and ∠ABD; ∠DBE
and ∠ABD; ∠ABF and
∠EBF; ∠ABC and ∠CBE;
∠FBC and ∠DBC; ∠FBE
and ∠DBE
Complementary
angles
none
∠ABF and ∠CBD;
∠DBE and ∠CBD
Angles with the
same measure
216
4
5
SpringBoard® Integrated Mathematics I, Unit 3 • Lines, Segments, and Angles
SpringBoard® Integrated Mathematics I, Unit 3 • Lines, Segments, and Angles
© 2017 College Board. All rights reserved.
Review the definitions of complementary
and supplementary angles as well as
those of radius, chord, and diameter of a
circle. Challenge students to add
diagrams of these to their KWL Charts.
Lesson 12-2
More Geometric Figures
ACTIVITY 12
continued
© 2017 College Board. All rights reserved.
Developing Math Language
ACTIVITY 12 Continued
Lesson 12-2
More Geometric Figures
ACTIVITY 12
5–7 Activating Prior Knowledge,
Create Representations, Interactive
Word Wall, Marking the Text, KWL
Chart To ensure that students
understand the definitions on this page,
you can ask questions such as the
following.
continued
A chord of a circle is a segment with both endpoints on the circle.
My Notes
A diameter is a chord that passes through the center of a circle.
A radius is a segment with one endpoint on the circle and one endpoint at
the center of the circle.
• What is the longest chord of a circle?
• How many ways can you describe
Point O in relation to the other
points and line segments in the
figure?
• What are two congruent line
segments in the figure?
5. In the circle below, draw and label each geometric term. Sample answer:
a. radius OA
B
b. chord BA
c. diameter CA
A
O
C
In Item 7, note that it is not appropriate
to refer to either circle as “Circle P.”
6. Refer to your drawings in the circle above. What is the geometric term
for point O? center
Call attention to the term justify in the
Academic Vocabulary and note the need
for evidence.
7. The circles below are concentric, meaning that they have the same
center. The center of both circles is point P.
Differentiating Instruction
a. Construct viable arguments. Explain why circle P is not an
appropriate name for the smaller circle.
Some students may benefit from a
more concrete approach to the
definitions on this page. Provide a
diagram of a circle with several radii,
chords, and diameters on which you
have labeled their measures. Then ask
students to state the length of a
diameter or to name the line segment
with a given measure.
The name is not appropriate because it is ambiguous. “Circle P”
could refer to either the smaller circle or the larger circle because
these circles have the same center.
© 2017 College Board. All rights reserved.
© 2017 College Board. All rights reserved.
b. Propose an alternate name for the smaller circle that would be
appropriate. Justify your choice.
Sample answer: circle P with radius PQ; This name is appropriate
because it describes the smaller circle but not the larger circle.
ACADEMIC VOCABULARY
When you justify a choice, you
provide evidence that shows that
your choice is correct or
reasonable.
Q
P
R
Activity 12 • Geometric Figures
217
Activity 12 • Geometric Figures
217
ACTIVITY 12 Continued
Lesson 12-2
More Geometric Figures
ACTIVITY 12
Check Your Understanding
Debrief students’ answers to these items
to ensure that they understand the
meaning of the terms used in this lesson
and know how to draw and label the
figures described in this lesson.
continued
My Notes
Check Your Understanding
8. Compare and contrast the terms acute angle, obtuse angle, right angle,
and straight angle.
Answers
8. Sample answer: All refer to angles
that measure no more than 180°.
Right angle and straight angle refer
to angles with an exact measure.
Acute angles and obtuse angles can
have a range of measures.
9. a. 48°
b. 138°
10. Sample answers:
a. PA
b. BC
9. The measure of ∠A is 42°.
a. What is the measure of an angle that is complementary to ∠A?
b. What is the measure of an angle that is supplementary to ∠A?
MATH TIP
You can use a compass to draw a
circle. You can also draw circles and
other geometric figures by
choosing the GeoGebra-CAS tab
from the toolbox on SpringBoard
Digital.
B
LESSON 12-2 PRACTICE
11. Classify each segment in circle O. Use all terms that apply.
A
P
10. Draw a circle P.
a. Draw a segment that has one endpoint on the circle but is not a
chord.
b. Draw a segment that intersects the circle in two points and contains
the center but is not a radius, diameter, or chord.
a. AF
A
b. BO
C
B
C
c. CO
O
d. DO
ASSESS
e. EO
Students’ answers to the Lesson Practice
items will provide a formative
assessment of their understanding of
describing angles and angle pairs and
identifying and naming parts of circles,
and of students’ ability to apply their
learning.
f. CE
F
E
13. Name two angles that appear to be obtuse.
14. Make sense of problems. Can two obtuse
angles be complementary to each other?
Explain.
ADAPT
You may wish to use the Teacher
Assessment Builder on SpringBoard
Digital to create custom assessments or
additional practice.
218
K
L
M
P
N
15. Model with mathematics. Is itpossible
for a pair of nonadjacent
angles to share vertex A and arm AB? If it is possible, draw an example.
If it is not possible, explain your answer.
Refer back to the graphic organizer the
class created when unpacking
Embedded Assessment 1. Ask students
to use the graphic organizer to identify
the concepts or skills they learned in this
lesson.
See the Activity Practice on page 231
and the Additional Unit Practice in the
Teacher Resources on SpringBoard
Digital for additional problems for this
lesson.
J
218
SpringBoard® Integrated Mathematics I, Unit 3 • Lines, Segments, and Angles
LESSON 12-2 PRACTICE
11. a. chord
b. radius
c. radius
d. radius
e. radius
f. diameter, chord
12. Sample answer: ∠PKJ and ∠JKL,
∠JKP and ∠PKM, ∠JKL and
∠LKM
13. Sample answer: ∠JKL, ∠PKM
14. No. The sum of the measures of
complementary angles is 90°, and
the measure of a single obtuse
angle is greater than 90°. So, two
obtuse angles cannot be
complementary.
15. Yes, it is possible. Sample answer:
∠BAC and ∠BAD
B
C
A
SpringBoard® Integrated Mathematics I, Unit 3 • Lines, Segments, and Angles
D
© 2017 College Board. All rights reserved.
12. Name three pairs of supplementary angles.
© 2017 College Board. All rights reserved.
The figure below includes PL and JM . Use the figure for Items 12–13.
Short-cycle formative assessment items
for Lesson 12-2 are also available in the
Assessment section on SpringBoard
Digital.
Check students’ answers to the Lesson
Practice to ensure that they understand
how to name and classify angles, radii,
chords, and diameters. If they have not
mastered this skill, have students work
together to create graphic organizers for
each term.
D