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Classifying Triangles by Angles and Sides Name: _____________________________ Geometry LESSON 4-1 Acute Triangle Right Triangle Obtuse Triangle all acute angles Equiangular Tri. one right angle 60 60 60 one obtuse angle all angles o Classify each triangle by its angle measures. Remember, there are 180 in every triangle. 2. 1. 3. Classify:_____________ Classify: _________________ Classify:___________________ 32 27 19 65 25 62 third angle = _______ third angle = _______ third angle = _______ Classify:_____________ Classify: ______________ Classify:_______________ Use the figure to classify each triangle by its angle measures. 4. DFG $ 5. DEG % 6. EFG ' & Classifying Triangles by Sides Page 2 LESSON 4-1 Equilateral Triangle Isosceles Triangle Scalene Triangle all sides congruent Step 1 Step 2 Find the value of x. QR RS 4x 3x 5 x5 at least two sides congruent no sides congruent 2 Def. of segs. Substitution Simplify. X X Use substitution to find the length of a side. 4x 4(5) Substitute 5 for x. 20 Simplify. 1 Each side length of QRS is 20. 3 Classify each triangle by its side lengths. 7. EGF is _____________________ $ 8. DEF is _____________________ % 9. DFG is _____________________ ' Find the side lengths of each triangle. _ X _ X _ 10. & 11. X X 2 x - 7x + 19 Equation: ________________________ x = _______ Side length = _________ X Equation: ________________________ x = _______ Side lengths = ________, _________ Classifying Triangles Page 3 LESSON 4-1 Practice A Match the letter of the figure to the correct vocabulary word in Exercises 1–4. 1. right triangle A. B. C. D. 2. obtuse triangle 3. acute triangle 4. equiangular triangle Classify each triangle by its angle measures as acute, equiangular, right, or obtuse. (Note: Give two classifications on # 7.) 60 5. 6. 45° 7. 30° 45° 60° 14° 136° 60° a b congruent sides. 8. An isosceles triangle has triangle has three congruent sides. 9. A(n) triangle has no congruent sides. 10. A(n) Classify each triangle by its side lengths as equilateral, isosceles, or scalene. (Note: Give two classifications on #13.) 12. 11. 13. 1 2 2.5 a Find the side lengths of the triangle. Equation: _________________________ x+2 ! x = _______ 14. AB # 15 AC b X6 17 15 " BC 15. The New York City subway is known for its crowded cars. If all the seats in a car are taken, passengers must stand and steady themselves with railings or handholds. How many hand straps could have been made from 99 inches of steel? 21 14 in. 14 in. 5 in. __________ G.1.A Classifying Triangles Page 4 LESSON 4-1 Practice B $ Classify each triangle by its angle measures. (Note: Some triangles may belong to more than one class.) 50° ! 100° " 40° 1. ABD 2. ADC ______________ _______________ 3. BCD # _______________ ' ( Classify each triangle by its side lengths. 4. GIJ 5. ______________ 3X 0.4 7. 2 HIJ _______________ 6. ) 6.9 GHJ * _______________ 0 X 0.1 X 1.4 1 Equation: _____________________________ x = _______ PQ = _______ QR = _______ RP = _______ 8. 3 2N 3 3–4 4 7N 10N 21–4 5 1 __ ST = _______ TU = _______ US = _______ 4 9. Use Chelsea works the kitchentoofdraw Pizza Today job of is to a ruler andin a compass a Pro. triangle withher sides 3 cm, 4 cm, and 5 cm. 6 cmof the cut pizza smallsegment. triangles.Then, She uses a cutting machine, First drawinto a 5-cm set your compass to 3 cm and make an arc from one end 5.7 cm so every triangle comesset outyour the compass same. The shows an an arc from the other 5-cm segment. Finally, to figure 4 cm and make 4 cmend of the 5-cm example. Mark She has beenwhere told tothe cutarcs 3 pizza triangles for every guest. segment. the point intersect. Connect this point to the ends of the 5-cm segment. There will be 250 guests. If the pizza comes in squares with 20-centimeter sides and she doesn’t waste any pizza, how many squares of pizza will Chelsea have to cut up? __________ CM CM CM Page 5 = show work! Choose the best answer. ‹__› 1. Which list shows all the segments on AC that contain the point B ? A B C D _ A B C D AC _ AB , _ AB , _ AB , _ _ BC , _ AC , _ AC , BD _ AD , _ AD , _ _ BC , BD _ _ _ BC , BD , CD 2. M is between R and S. If RM 21, RS 15x 3, and MS 9x 12. Equation: ____________________________ _ 3. K is the midpoint of VW . If KV 3x and KW 5x 10. 6. Two vertical angles are also complementary. What is the measure of one of the two vertical angles? F 90 H 45 G 50 J 25 7. The area of a square is 16 square units. What is the perimeter? A 4 units C 16 units B 8 units D 32 units 8. The midpoint of a segment is (8, 5). If Draw and label diagram. one endpoint is (0, 1),awhat is the other endpoint? F (16, 9) H (4, 2) G (8, 3) J (4, 3) x = _______ RS = _______ MS = _______ 9. To the nearest tenth, what is the distance Draw andand label(3, a diagram. between (7, 4) 1)? A 5 C 20.5 B 10.4 D 54.5 Equation: ____________________________ 10.x =Which _______ KV = _______ KW = _______ coordinate pair represents the image of (9, 10) reflected over the 4. Which appears to be an obtuse angle? x-axis? 2 F (9, 10) H (9, 10) 4 J (10, 9) G (9, 10) 3 11. What is the next figure in the pattern? 1 F PQR G PSQ 0 H R J P A C B D 5. Which two angles are supplementary to RLK? 12. For which statement is the converse false? 1 F If Mary can swim, then she can swim 0 2 the crawl. , G If it is raining outside, then the + temperature is above freezing. H If Greg has two children, then he has one son and one daughter. __________ and __________ J If Carolyn can stand up, then she can walk.