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© Glencoe/McGraw-Hill 5–1 NAME DATE PERIOD NAME 5–1 Study Guide DATE Classifying Triangles Classifying Triangles Triangles are classified in two different ways, either by their angles or by their sides. Classify each triangle by its angles and by its sides. 1. 60° Classification of Triangles Angles Sides all acute angles scalene no two sides congruent obtuse one obtuse angle isosceles at least two sides congrent right one right angle equilateral all sides congruent 35° acute, equilateral right, scalene 27 ° D 4 cm 20 cm 36° 11 m 30 cm 100° 22 cm E 60° M n DEF is obtuse and scalene. 60° isosceles, acute N n MNO is acute and equilateral. 7. 2. n XYZ, m/ X 5 60, XY 5 YZ 5 ZX 5 3 cm scalene, obtuse 8. 32° 130° 42° 9. 60° 18° isosceles, acute 45° 60° 45° 60° 3. n DEF, m/ D 5 150, DE 5 DF 5 1 inch obtuse, scalene acute, equilateral isosceles, right Z L F Geometry: Concepts and Applications D K M X right, scalene 4. n GHI, m/ G 5 30, m/ H 5 45, GH 5 4 cm Y acute, equilateral obtuse, isoceles 5. n NOP, m/ N 5 90, NO 5 NP 5 2.5 cm 6. n QRS, m/ Q 5 100, QS 5 1 inch, QR 5 1}1} inches P I G R 10. right scalene 11. obtuse isosceles 12. right isosceles 13. right equilateral 2 obtuse, scalene not possible O right, isosceles Q © Glencoe/McGraw-Hill Make a sketch of each triangle. If it is not possible to sketch the figure, write not possible. H N obtuse, scalene E 179 S Geometry: Concepts and Applications © Glencoe/McGraw-Hill 180 Geometry: Concepts and Applications (Lesson 5-1) A2 Use a protractor and ruler to draw triangles using the given conditions. If possible, classify each triangle by the measures of its angles and sides. 1. n KLM, m/ K 5 90, KL 5 2.5 cm, KM 5 3 cm 72° 72° 38° 60° 2.3 cm 102 ° 6. 50° 11 m isosceles, obtuse 5. 15 m 50° 40° 25 ft Answers 5 cm 40° 4 cm 80° 51° 16 ft 100° 16 ft 5 cm 55° 6 in. 4. Examples: Classify each triangle by its angles and by its sides. O F 1 2 3. 3 cm 60° 60° acute 2. 6 in. 6 in. PERIOD Skills Practice © Glencoe/McGraw-Hill 5–1 NAME DATE PERIOD Practice Classifying Triangles wB A w, B wC w, w AC w 2. angles of the triangle /A, /B, /ACB /ACB 4. base angles /A, /B 5. side opposite /BCA DATE PERIOD wB A w Key Terms triangle a figure formed when three noncollinear points are connected by segments vertex of a triangle the vertex of an angle formed by two adjacent segments of a triangle acute triangle a triangle with all acute angles obtuse triangle a triangle with one obtuse angle right triangle a triangle with one right angle scalene triangle (SKAY•leen) a triangle with no sides congruent isosceles triangle (eye•SAHS•uh•LEEZ) a triangle with at least two sides congruent equilateral triangle (EE•kwuh•LAT•ur•ul) a triangle with all sides congruent Reading the Lesson 1. Supply the correct numbers to complete each sentence. 2 acute angle(s), ______ 0 right angle(s), and ______ 1 a. In an obtuse triangle, there are ______ obtuse angle(s). wC A w, w BC w 3 acute angle(s), ______ 0 right angle(s), and ______ 0 b. In an acute triangle, there are ______ obtuse angle(s). 7. angle opposite w AC w /B 2 acute angle(s), ______ 1 right angle(s), and ______ 0 c. In a right triangle, there are ______ obtuse angle(s). 2. Determine whether each statement is always, sometimes, or never true. If the statement is not always true, explain why. Classify each triangle by its angles and by its sides. 8. a. A right triangle is scalene. isosceles. 9. Sometimes; a right triangle may be scalene or Geometry: Concepts and Applications b. An obtuse triangle is isosceles. isosceles or scalene. Sometimes; an obtuse triangle may be c. An equilateral triangle is a right triangle. all angles measuring 60°. right, scalene d. An equilateral triangle is isosceles. Never; an equilateral triangle has always Helping You Remember equiangular, equilateral 10. Find the measures of the legs of isosceles triangle ABC if AB 5 2x 1 4, BC 5 3x 2 1, AC 5 x 1 1, and the perimeter of nABC is 34 units. 14 units © Glencoe/McGraw-Hill 181 Geometry: Concepts and Applications 3. A good way to remember a new mathematical term is to relate it to a nonmathematical definition of the same word. How is the use of the word acute, when used to describe acute pain, related to the use of the word acute when used to describe an acute angle or an acute triangle? Sample answer: Both are related to the meaning of acute as sharp. An acute pain is a sharp pain, and an acute angle can be thought of as an angle with a sharp point. In an acute triangle, all of the angles are acute. © Glencoe/McGraw-Hill 182 Geometry: Concepts and Applications (Lesson 5-1) A3 6. congruent sides Answers 3. vertex angle NAME Reading to Learn Mathematics Classifying Triangles For Exercises 1–7, refer to the figure at the right. Triangle ABC is i A isosceles with AB . AC and AB . BC. Also, XY wB w. Name each of the following. 1. sides of the triangle 5–1