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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 2: Triangles
As you work through the tutorial, complete the following questions.
1. The total weight of Dijit and the glider is __________ lb.
2. The area of the sail needed for the glider to carry Dijit safely
is _________ ft 2.
3. A quadrilateral has __________ sides and __________ angles.
4. In the description of the sail, the length along the keel is __________ ,
and the width of the support rod is __________ .
5. A(n) __________ triangle is a triangle that contains a ________ -degree
angle.
6. A triangle that has two equal sides is called a(n) __________ triangle.
Key Words:
Quadrilateral
Area
Triangle
Angle
Right triangle
Isosceles triangle
Scalene triangle
Learning
Objectives:
• Dissecting a
quadrilateral into
sets of triangles
• Defining a right
triangle
• Defining an
isosceles triangle
• Defining a
scalene triangle
7. Can a triangle be classified as both an isosceles triangle and a right
triangle? __________ If so, what measurement must one of the angles
have? __________
8. When you draw a triangle, how do you show that two sides are equal?
________________________________________________________________
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9. A(n) __________ triangle has __________ equal sides.
10. Can a scalene triangle also be a right triangle? ______________________
11. What are two ways to classify triangles? __________ __________
destination
MATH
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 2: Triangles
Use this figure to answer questions 1–8.
A
1. Is figure AFCDE a quadrilateral? Why
or why not? ______________________
B
E
F
2. Triangle nBFC contains two equal
sides. What kind of triangle is this?
C
a. right triangle
D
b. scalene triangle
c. isosceles triangle
d. scalene right triangle
3. Which triangle(s) are isosceles right triangle(s)? ______________________
4. Which triangle(s) are scalene right triangle(s)? _________________________
5. Triangle nCFD has three unequal sides. What kind of triangle is it?
______
a. right triangle
b. isosceles triangle
c. scalene triangle
d. isosceles right triangle
6. Triangle nAFE contains three unequal sides and a 90º angle. Which of
a. right triangle
b. scalene triangle
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the following best describes this triangle? ______
c. isosceles right triangle
d. scalene right triangle
7. Triangle nABE is a __________ triangle.
8. AEDF is divided into two triangles, nAEF and __________ .
destination
MATH
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 2: Triangles
As you work through the tutorial, complete the following questions.
1. Dividing a rectangle along its diagonal will result in two _________
having __________ areas.
Key Words:
Triangle
Area
Rectangle
Parallelogram
Equilateral triangle
Equiangular triangle
2. The area of a rectangle equals __________ . So, one half of the area of a
rectangle,
1
}}
2
(b 3 h), equals the area of a __________ .
3. The height of a triangle is a ___________________ segment drawn from a
______________ of the triangle to the opposite side.
4. Dijit divides the sail into two equal triangles and finds the area of one of
the triangles. How does Dijit find the total area of the sail? ____________
________________________________________________________________
Learning
Objectives:
• Relating the area
of a triangle to
the area of a
rectangle
• Identifying the
height of a
triangle
• Calculating the
area of a triangle
• Defining an
equilateral
triangle
5. What is the total area of the glider sail? ______________________________
6. How many degrees are contained in a triangle? ______________________
7. An equiangular triangle has _________ equal _________8 angles.
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8. An equilateral triangle has __________ __________ sides.
9. Can a triangle be equiangular, but not equilateral? _________
Explain. ________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
destination
MATH
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 2: Triangles
1. What formula is needed to calculate the area of
a triangle?
B
________________________________
20
2. Which of the following represents
the base of the triangle nABC ?
A
__________
a. AB
b. BC
c. AD
13
12
16
D
7
C
d. AC
3. Which of the following represents the height of the triangle nABC ?
__________
a. BC
b. BD
c. AD
d. AC
4. What is the measure of /BDA? ____________________________________
5. What kind of triangle is nBDA?
__________________________________
6. What is the length of the base of nABC ?
7. What is the height of nABC ?
__________________________
____________________________________
______________________________________
9. What is the area of nBDC ?
______________________________________
10. What is the area of nBDA?
______________________________________
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8. What is the area of nABC ?
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MATH
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 2: Triangles
As you work through the tutorial, complete the following questions.
1. What instrument is used to measure angles? __________________________
2. An angle that measures more than __________ degrees but less
than _________ degrees is called a(n) __________ angle.
Key Words:
Right angle
Right triangle
Straight angle
Acute angle
Acute triangle
Obtuse angle
Obtuse triangle
3. The sum of the measures of the angles of a triangle is __________ .
4. A right triangle contains exactly __________ right angle.
5. A straight angle has a measurement of __________ .
6. Can a triangle contain a straight angle? ____________________________
7. Explain your answer to Question 6 using your answers to Questions 3
and 5. __________________________________________________________
Learning
Objectives:
• Applying the
triangle sum
formula to find
missing angle
measures
• Identifying right
triangles
• Identifying acute
triangles
• Identifying obtuse
triangles
__________________________________________________________________
8. An acute triangle has __________ __________ angles.
9. An angle that measures more than __________ degrees but less than
_________ degrees is called an obtuse angle.
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10. An obtuse triangle has __________ __________ angle.
11. Can an obtuse triangle have 2 obtuse angles? __________ Explain your
answer. __________________________________________________________
destination
MATH
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 2: Triangles
Answer each question using the following
triangles: nAFB, nAFE, nBFC, nCFD,
or nDFE.
1. Which triangle(s) have right angles?
A
B
E
F
__________________________________
2. Which triangle(s) can be classified as
C
D
right triangles? ____________________________________________________
3. Which triangle(s) have all acute angles? ______________________________
4. Which triangle(s) can be classified as acute? ________________________
5. Which triangle(s) have obtuse angles? ______________________________
6. Which triangle(s) can be classified as obtuse? ________________________
7. Name one straight angle in the figure. ______________________________
8. a. Which two adjacent triangles can be combined to form a third
triangle? ______________________________________________________
b. Use the vocabulary of this unit to describe the triangles you listed in
part a.
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______________________________________________________________
______________________________________________________________
destination
MATH
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 2: Triangles
Classifying Triangles by Sides
C
In the figure on the right, CD 5 CA
and /DCA 5 110º.
A
E
D
1. What kind of triangle is nACD ?
__________________________________
2. Draw CE. Lines CD, CE, and DE all have different lengths. What kind of
triangle is nCED ?
______________________________________________
3. Draw BE perpendicular to CA. How many degrees are in /ABE ? ______
4. What kind of triangle is nCBE ?
__________________________________
Exploring the Area of a Triangle
In nCBE above, BE 5 5 cm, and CB 5 8 cm.
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5. Find the area of nCBE. Show your work below.
6. Which line segment did you use as the height? ______________________
7. Is triangle nCBE equilateral? ______________________________________
Explain your answer. ______________________________________________
__________________________________________________________________
destination
MATH
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Name _______________________________________
Date ___________________________
Classifying Triangles by Angles
Triangle nCDA is an isosceles triangle. The angles opposite the equal sides of
an isosceles triangle are also equal.
8. Find m/CDA and m/CAD.
______________________________________
9. Besides isosceles, what other term could describe nCDA?
____________
10. If /DCE is less than 90º, what kind of triangle is nCDE ? ______________
Putting It All Together
11. The headings across the top row of the table below are terms that classify
triangles by their sides. The headings in the first column are terms that
classify triangles by their angles. For each pair of conditions, draw a
triangle. If it is not possible to draw a triangle that satisfies both
conditions, write not possible for that triangle.
Triangles
Scalene
Isosceles
Equilateral
Acute
Right
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Obtuse
destination
MATH
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 2: Triangles
Study the diagram and answer each question below. In the figure, nABC is
a scalene triangle with AB 5 4, AC 5 6.2, and BC 5 6.6. Point D is the
midpoint of BC.
A
B
D
C
1. What is a scalene triangle? ________________________________________
2. Can a scalene triangle also be isosceles? __________ Why or why not?
__________________________________________________________________
3. nABC is an acute triangle. Identify another acute triangle in the figure.
__________________________________________________________________
4. Identify an obtuse triangle in the figure. ______________________________
5. What are the lengths of BD and DC ? ________________________________
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6. Draw AE perpendicular to BC. If AE 5 3.8, find the area of nABC to the
nearest tenth. Show your work in the space provided.
7. What is the area of nABD to the nearest tenth? Show your work below.
destination
MATH
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Name _______________________________________
Date ___________________________
Study the diagram and answer each question below. In the figure, nABC is
a scalene triangle with AB 5 4, AC 5 6.2, and BC 5 6.6. Point D is the
midpoint of BC and the height of nABD is AE 5 3.8.
A
B
E
D
C
8. What is the area of nADC to the nearest tenth? Show your work below.
9. What do you notice about the areas of nABD and nADC ? Explain your
observation. ______________________________________________________
________________________________________________________________
10. In the space at the right, draw an isosceles right triangle, nDEF.
Mark the hypotenuse, the side opposite the right angle, as EF.
a. Use a protractor to measure the angles of nDEF to
the nearest degree. Label the measure of each angle.
b. Use like markings to show which sides of nDEF are equal.
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c. Draw a second triangle adjacent to the first. Use the
hypotenuse, EF, as one side of the new, equiangular
triangle, nEFG.
d. Use like markings to show which sides of nEFG are equal.
e. Use a protractor to measure the angles of nEFG to the
nearest degree. Label the measure of each angle.
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