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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? ________________________________________________________________ © RIVERDEEP, Inc. 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 61 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 © RIVERDEEP, Inc. 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 62 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. © RIVERDEEP, Inc. 8. An equilateral triangle has __________ __________ sides. 9. Can a triangle be equiangular, but not equilateral? _________ Explain. ________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ destination MATH 63 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? ______________________________________ © RIVERDEEP, Inc. 8. What is the area of nABC ? destination MATH 64 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. © RIVERDEEP, Inc. 10. An obtuse triangle has __________ __________ angle. 11. Can an obtuse triangle have 2 obtuse angles? __________ Explain your answer. __________________________________________________________ destination MATH 65 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. © RIVERDEEP, Inc. ______________________________________________________________ ______________________________________________________________ destination MATH 66 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. © RIVERDEEP, Inc. 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 67 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 © RIVERDEEP, Inc. Obtuse destination MATH 68 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 ? ________________________________ © RIVERDEEP, Inc. 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 69 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. © RIVERDEEP, Inc. 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. destination MATH 70