Download Geometry Investigations

Investigation #1
Grades 6-7
Standards: 6MG 2.1
Part One: Identifying Angles
An acute angle has a measure greater than _____ degrees and less than
______degrees.
1. An obtuse angle has a measure greater than _____degrees but less than
_____degrees.
2. A straight angle has a measure of _____degrees.
3. A right angle has a measure of _____ degrees.
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Part Two: Use the corner of a blank piece of paper. Draw a line from the
corner and measure the two angles that are created.
Measurement #1: _____ + ______=_____
Measurement #2: _____ + _____ = _____
Measurement #3: _____ + _____ = _____
Measurement #4: _____ + _____ = _____
What do we notice about the sum of our angle measures?
_____________________________________________________________.
These angles are called _____________________ angles and always add to
_______.
You Try!
Identify below, the pair of complementary
angles
You Try!
Find the missing angle measure.
A
x°
C
B
D
62°
E
x = ___________________
Angles _________ and _____________.
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Part Three:
Measurement #1: _____ + ______=_____
Measurement #2: _____ + _____ = _____
Measurement #3: _____ + _____ = _____
Measurement #4: _____ + _____ = _____
What do we notice about the sum of our angle measures?
_____________________________________________________________.
These angles are called _____________________ angles and always add to
_______.
You Try!
You Try!
Identify below, the pair of
Find the missing measure.
supplementary angles.
1
4
25°
2
x°
60°
3
x = __________
Angles ________ and ________.
Angles ________ and ________.
Angles ________ and ________.
Angles ________ and ________.
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Independent Practice:
Find the missing angle measures
2.
1.
x°
3.
35°
4.
20°
x°
x°
125°
y°
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Worked Out Solutions
Part 1:
You Try!
A C B D x°
62°
E Complementary angles creates a 90°
angle, therefore the pair of
complimentary angles are
∠ABD
and
∠DBF
Complementary angles add to 90° .
x ° + 62° = 90°
x ° + 62° − 62° = 90° − 62°
x ° = 28°
Part 2:
You Try!
1
4
2
25°
x°
60°
3
The supplementary angle must add up to
180°.
25° + 60° + x ° = 180°
85° + x ° = 180°
∠ 1 and ∠ 2
85° − 85° + x ° = 180° − 85°
x ° = 95°
∠ 2 and ∠ 3
∠ 3 and ∠ 4
∠ 4 and ∠ 1
Independent Practice: Worked Out Solutions
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1.
2.
x ° The missing angle measure is 40°
Because the two angles are vertical angles
their measures are equal.
35 ° x ° + 35° = 90°
x ° + 35° − 35° = 90° − 35°
x ° = 55°
4.
3.
20° x ° x ° 125 ° y° x ° + 20° = 180°
x ° + 20° − 20° = 180° − 20°
x ° = 160°
x ° + 125° = 180°
x ° + 125° − 125° = 180° − 125°
x ° = 55°
If x is 55° , then y is its
supplement.
180° − 55° = y°
125° = y°
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Investigation #2
Area of a Triangle
Standards: MG 1.3
Remind students how to find the area of a parallelogram: A = bh
1. Have students draw a diagonal across the parallelogram.
2. Cut out along the diagonal.
3. Students should notice that two triangles have been formed.
4. Prompt students to discover the area formula.
*”If the area of a parallelogram is A = bh , then how can we describe the area
1
of this triangle?” (It would be of the parallelogram)
2
1
*If the area of this triangle is of the area of the parallelogram, how can we write
2
1
the area formula? ( A = bh )
2
Example #1:
Find the area of the triangle in centimeters.
bh
1
A=
bh
2
2
12 cm • 6 cm
1
A = (12 cm )(6 cm ) A =
2
2
2 • 6 • 6 • cm • cm
A = (6 cm )(6 cm )
A=
2
A = 36 cm 2
2
A = 36 cm
A=
6
12
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You Try#1
Find the area of the triangle in meters.
You Try#2
Find the area of the triangle in inches.
5
4.2
20
10
Independent Practice:
1. Find the area of the triangle.
2. Find the area of the triangle.
10 in
3 in
3. What is the area of the shaded
figure?
20 ft
8 cm
11 ft
1
4 cm
2
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Worked Out Solutions:
You Try#1
YouofTry!
Find the area
the triangle in meters.
You Try#2
Find the area of the triangle in inches.
5
4.2
20
10
1
A = bh
2
1
A = (20 m )(5 m )
2
A = (10 m )(5 m )
1
(10 m )⎛⎜ 4 2 m ⎞⎟
2
⎝ 10 ⎠
A=
1
(10 m )⎛⎜ 42 m ⎞⎟
2
⎝ 10 ⎠
1 • 10 • 42 • m • m
A=
2 • 10
1• 2 • 2 • 3 • 5 • 7
A=
2•2•5
A=7
A=
A = 50 m 2
1. Find the area of the triangle.
2. Find the area of the triangle.
10 in
8 cm
3 in
1
4 cm
2
1
⎛ 1
⎞
1
⎛ 1
⎞
(
)
A
=
8
cm
4
cm
⎜
⎟
A = (8 cm )⎜ 4 cm ⎟
2
2
⎝
⎠
2
⎝ 2
⎠
9
1
⎛
⎞ A = (4 cm )⎛⎜ cm ⎞⎟
A = (4 cm )⎜ 4 cm + cm ⎟
⎝2
⎠
2
⎝
⎠
36
A = 16 cm 2 + 2 cm 2
A=
cm 2
2
A = 18 cm 2
A = 18 cm 2
1
(10 in )(3 in )
2
A = (5 in )(3 in )
A=
A = 15 in 2
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3. What is the area of the shaded
figure?
20 ft
1
(20 ft )(11 ft )
2
A = (10 ft )(11 ft )
A=
11 ft
A = 110 ft 2
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Investigation #3
Transversals/ Alternate Interior Angles
Standards: MG 2.0, 2.1
MR 2.0, 2.4
• Explain to students the definition of a transversal
• As students look at the picture of a transversal (see below)
they should notice that 8 angles are formed.
• Have the discussion about the types of angles, i.e. which
angles are complimentary and which angles are
supplementary.
• Have students cut the picture in half, so that the angles will
overlap. From this students will be able to see the
corresponding angles
• From here a discussion can begin about interior, alternate
interior, exterior and alternate exterior angles.
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p
11
34
55
78
22
m
34
n
66
78
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