NAME DATE PERIOD Name ___________________________________ Hour ______ 4-1 Skills Practice 4-1 and 4-2 Review Worksheet Classifying Triangles 4-1 Classifying Triangles Classify each triangle as acute, equiangular, obtuse, or right. 1. 60° 4. 2. 60° 60° 95° 90° 45° 50° 5. 50° 80° 3. 40° 40° 70° 6. 50° 30° 50° 55° 55° 100° Classify each triangle as equilateral, isosceles, or scalene. 7. !ABE 8√2 8. !EDB E Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 9. !EBC 8 D C 10. !DBC 11. ALGEBRA Find x and the length of each side if !ABC is an isosceles −− −− triangle with AB # BC. 12. ALGEBRA Find x and the length of each side if !FGH is an equilateral triangle. # 4x - 3 " B 9 A x+2 ( 3x + 10 2x + 5 ' $ x =ALGEBRA ______________ 13. Find x and the length of each side if !RST is an isosceles −− −− AB = _____________ triangle with RS # TS. 5x - 8 ) 4x + 1 = _______________ 14.x ALGEBRA Find x and the length of each side if !DEF is an equilateral triangle. FG = _____________ BC = _____________ 3 GH = _____________ & 9x + 2 AC = _____________ FH = ______________ 3x - 1 5x - 21 2x + 6 4 6x + 8 5 Chapter 4 % 43 7x - 39 ' Glencoe Geometry NAME DATE PERIOD 57° ware - Infinite Geometry Name___________________________________ FNGLE INDING ANGLE MFind EASURES Find the of the numbered NT HELP FINDINGHA MEASURES the measure ofmeasure the numbered angles. FINDING ANGLE M EASURES Find the measure of theangles. numbered angles. STUDENT ELP Kuta Software - Infinite Geometry Name___________________________________ NET HOMEWORK 31. 32. 33. ER HELP Pin a Triangle 31. HOMEWORK HELP 1 33. Date________________ 31. 32. 32. 33. Period____ 1 1 4-1site Triangle Angle Sum Visit 1 1 our Web 1 site our Web Visit site 56! Angles in a Triangle Date________________ Period____ 56! cdougallittell.com 56! com www.mcdougallittell.com 3 measure of each angle indicated. 3 2 Find each missing angle. with Exs. 31–33. 3 of Triangles 50! 3 3 40! 2 3. 3 2 for help with Exs.Angles 31–33. 40! 50! 95! 40!50! 13. the measure 15.1 2 95! 14. 42! angle indicated. 95!45! Find of each 42! 1 45!2 42! 45! 1 2 Find the measure of each numbered 3) 2) angle. ? 1) LOGICAL 2) LOGICAL REASONINGComplete Complete the statement using always, sometimes, REASONING the statement using always, sometimes, 4-2 INT Practice 1.xor never. 65° 2. ? xy USING A The variable expressions represent the angle 40° xLGEBRA USING ALGEBRA The variable the angle y EASONING UOGICAL SING Aexpressions LGEBRA Therepresent variable expressions represent the anglesometimes, LOGICAL R L RComplete EASONING the Complete statement the using always, using sometimes, always, orynever. 1statement 72° measures of a triangle. Find the measure of each angle. Then classify the 20° 2 of measures triangle. Find the measure of each angle. Then40° classify the or anever. or never. measures of a triangle. Find the measure of each angle. Then classify the ? 22. An isosceles triangle is an equilateral triangle. !!!!! by its ?!!!!!! 22. An isosceles triangle is angles. an its equilateral !!!!! triangle bytriangle its 1angles. triangle by angles. triangle. ?!!! an ?!!! an 22. An isosceles 22. An triangle isosceles is !!!!! triangle is !!!!! equilateral triangle. equilateral 57° 40° 55°triangle. ?!!! 23. obtuse triangle is !!!!! isosceles triangle. ?!!! 23. AnAn obtuse triangle isx° anan isosceles triangle. !!!!! 34. m™A = 35. m™R = x° 36. = 36. (x º 15)° = (x º130° ? 34. m™A =23. x° An obtuse 35.obtuse m™R = x°an isosceles 36. m™W (xm™W º 15)° 34.triangle m™A = x°triangle 35.triangle. m™R = x° = m™W 15)° ? ? ? 23. An is is an isosceles triangle. !!!!! !!!!! !!! !!! 24. An interior angle of a triangle and one of its adjacent exterior angles m™B of = a2x° = 7x° m™S = (2x º 165)° 24. An interior triangle and one ofm™S its adjacent exterior m™B = 2x°angle = 7x° m™Y = (2xm™Y º? 165)° m™Bm™S = 2x° = angles 7x° m™Y = (2x º 165)° are !!!!! supplementary. !!! An interior 24.angle An interior of a triangle angle of anda one triangle of itsand adjacent one ofexterior its adjacent angles exterior angles ? ?24. ° m™C = (2x m™C + 15)° m™T = x° m™Tm™Z are supplementary. !!!!!= !!!(2x m™C + 15)° m™T =+ x° 15)° = (2x = x°= 90°m™Z = 90° m™Z = 90° ?!!! ?!!! supplementary. are are !!!!! supplementary. ?!!! complementary. 25.each The acute angles of a right triangle !!!!! Find the value of!!!!! x.of Find measure. ?!!! 25. The acute angles a right triangle areare complementary. !!!!! 5) 18. 4) 16. 17. ?!!! ?!!!angle 25. The acute 25. angles The acute of a right angles triangle of a right are angle. triangle are !!!!! complementary. complementary. ? 26. A triangle has a right angle and an obtuse xy E !!!!! !!!!! !!! 3 shown. XTERIOR ANGLES Find theof measure of the exterior ? xy A 26. triangle has a right angle and an obtuse angle. x !!!!! !!! y E XTERIOR A NGLES Find the measure the exterior angle shown. E XTERIOR A NGLES Find the measure of the exterior angle shown. 4) 58° 3.3) m∠1 ?!!! ?!!!angle 1 26. A triangle 26. A triangle has a right has aand right anangle obtuse and angle. an obtuse angle. !!!!! 85° 2 IDENTIFYING PARTS OF!!!!! TRIANGLES Refer to the triangles in Exercises 16–21. 37. 38. 39. I37. DENTIFYING PARTS OF37. TRIANGLES Refer to the triangles 38. 38. 39. in Exercises 16–21. ! 137° 85° x39. 20° 4. m∠2 x ! 16–21. IDENTIFYING IDENTIFYING Pthe ARTS OF TP RIANGLES ARTS OF right TRefer RIANGLES to the Refer triangles tox !the in Exercises triangles in 16–21. Exercises 35° 27. Identify the legs and hypotenuse of any triangles. 38! 27. Identify 20° the legs and the hypotenuse 50° ? triangles.38! 38! of any right 39° triangles. 27.the Identify 27.the legs Identify andofthe hypotenuse legs and thetriangles. of hypotenuse any right of any right triangles. (2x 8)!the 5. m∠3 28. Identify legs"and base any isosceles Which 50° (2x " 8)! (2x of " 8)! ?isosceles 28. the legs and the base any isosceles triangles. Which isosceles 130°Identify ? 28. triangle has a base that is also the hypotenuse of a right triangle? (10x # 9)! (2xWhich " 21)! isosceles Identify the 28. legs Identify and the base legs and of any the isosceles base of any triangles. isosceles Which triangles. isosceles 31! the hypotenuse ! is also (10x # 9)! " 21)! # 9)! (2x " 21)! triangle has a base xthat of a right triangle?(10x (2x 31! x! 31! x! 130° ?base that (7x #is 1)!also Æ triangle has atriangle has# isa1)! also basethe that hypotenuse theof hypotenuse a right triangle? of a right triangle? 102° ? xy USING ALGEBRA (7x Use the graph. The segmentÆ AB (7x # y1)! xy USING ALGEBRA Use the graph. The segment AB Æ Æ y is a leg of40. isosceles triangle. xan xLGEBRA y U yright Aright AUse LGEBRA SING USING Use the graph. UseThe the segment graph. The ABsegment AB TECHNOLOGY geometry software to demonstrate the is a leg ofTan isosceles triangle. y Sum Find each measure. C Triangle (?, ?) 40. ECHNOLOGY Use geometry software to demonstrate the Triangle Sum 40. T ECHNOLOGY Use geometry software toy demonstrate the Triangle Sum is a leg of an is isosceles a leg of an right isosceles triangle. right triangle. C(?, ?) 6) 19. each numbered Theorem or theC.Exterior Angle Theorem. Describe your procedure. C (?, ?) 29. Find FindTheorem the coordinates ofangle. point Copy the graph or the Exterior Angle Theorem. Describe your procedure. Theorem or the Exterior Angle Theorem. Describe your procedure. C (?, ?) 29. Find the coordinates of point C. Copy the graph 2° FINDING angles. 100° ? ANGLE MEASURES Find the measure of the numbered FINDING ANGLE FINDING MEASURES ANGLE M Find EASURES the measure Find the of measure the numbered of theangles. numbered NT HELP STUDENT HELP ELP 31. 32. 33. 10. m∠5 102° 100° ? 35° 1 33. Pb site E31. RNET 32. 1 HOMEWORK HELP HOMEWORK HELP 1 31. 31. 32. 32. 33. 1 35°33. INT site l.com 11. m∠6 1 Visit Visit our Web site om our Web site –33. cdougallittell.com www.mcdougallittell.com 3. 42! with Exs. for31–33. help with Exs. 31–33. 1 1 3 42! 42! 3 2 95! 95! 42! 2 40! 340! 2 95! 56! 56! 1 50! 3 50! 1 2 40! 1 2 45! 3 245! 40! 45! 95! 8) 7)xy USING ALGEBRA The variable expressions represent 8)the 1angle 155° B 58°angle xy U Find each SING measure. A The variable expressions represent 155° xof xy Find measures a triangle. the measure of each angle.the Then classify the yLGEBRA 20° 56! 50! 1 45! 2 3 50! 1 2 3 64° C USING ALGEBRA USINGThe ALGEBRA variableThe expressions variable expressions represent60° the represent angle the angle measures of aits triangle. Find the measure of each angle. Then classify the triangle by angles. measures a triangle.ofFind a triangle. the measure Find the of measure each angle. of each Thenangle. classify Then the 60° classify the ? ofmeasures triangle its angles. 12. m∠1 by triangle 2 by its triangle angles. by its angles. 30° A D 20. 34. m™A = x° 35. m™R =21. x° 36. m™W?= (x º 15)° 22. m™A =34. x° m™A = 34. 35. m™R = x° 36. m™W (x º 15)°=36. 13.34. m∠2 ? x° m™A m™S = x° = 35.7x° m™R = 35. x° m™R = x°== 36. m™W (x º m™W 15)° = (x º 15)° m™B = 2x° m™Y (2x º 165)° 20° ? ° 356! angles. m™B = 2x°m™B =20° m™S = 7x°m™S = 7x° m™S m™Y = (2x m™Y º 165)° = 2x° = 7x° = (2x º m™Y 165)° = (2x º 165)° m™C = (2x + 15)°2x° m™B m™T = x° m™Z = 90° m™C = (2xm™C + 15)° m™T = x° m™Z = 90° = (2x m™C + 15)°= (2x + 15)° m™T = x° m™T = x° m™Z = 90° m™Z = 90° Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 6) the graph 6.5) m∠1 and sketch ¤ABC. 29. Find the 29. coordinates Find the of coordinates point C. Copy of point the C. graph Copy and sketch ¤ABC. and sketch ¤ABC. and sketch ¤ABC. 5 4.1 Triangles A (2, 2)?4.1and B (5, Angles 2)199 and199 7. m∠4 30. Find the coordinates of a point D that forms a Triangles 4.1 and Angles 199 2 A(2,Angles 2) B(5, Triangles 2) 7) 30. Find137° the coordinates of a point D that formsÆ a A?(2, 2) (5, 2) B (5, 2) different right triangle with leg AB . a forms Æ 30.isosceles Find the 30. coordinates Find the of coordinates a point D of that point Da that forms a A (2, 2) x B70° 118° 3 4 different isosceles right triangle with leg AB. Æ Æ 8. m∠3 Include a sketch with your answer. x different isosceles different right isosceles triangleright withtriangle leg AB. with leg AB . 6 1 36° 65° Include a sketch with your answer. x x ? Include a sketch Include with a your sketch answer. with your answer. 9. m∠2 68° 82° FINDING ANGLE MEASURES Find the measure of the numbered angles. 30° xy EXTERIOR ANGLES 14. CONSTRUCTION TheFind diagram shows of anthe exterior angle shown. the measure xy EXTERIOR 1PrCiAgRhatqsv rrxevsve3rRvceOd8.K 5 CMoaBd9e8 5wAiAtghM vIqnEf6i7nNi8tre7 QGYeXoEm9eatyrQyf.Q A NGLES Find the measure of the exterior angle shown. K2L0H18 1m eexterior K4uNtUaNshown. 9STo5fBtMwXa2rangle ee9 sLYLRCP.H g CAHlGlA xy the x example of Pratt Truss used in bridge EXTERIORy AENGLES XTERIOR Find ANGLES the measure Find the of measure the exterior of©J the angle shown. 145° 37. 38. 39. construction. Use the diagram to find m∠1. x! 37. 38. 39. 37. (2x " 8)! (2x " 8)! x! x! Chapter 40. 4 40. 37. (2x " 8)! 31! 31! x ! 38. 38. 38! 38! (2x " 8)! 38! 39. x! 39. x! x! 38! (10x # 9)! (2x " 21)! (10x # 9)! (10x # 9)! (10x(2x #" 9)!21)! (2x " 21)! (2x " 21)! 31! x ! (7x # 1)! (7x # 1)! (7x # 1)! (7x # 1)! Glencoe Geometry geometry software46 to demonstrate the Triangle Sum 31! TECHNOLOGY Use TECHNOLOGY Use geometry software toUse demonstrate the Triangle Sum 40. TECHNOLOGY 40. TECHNOLOGY Use geometry software geometry toyour demonstrate software to demonstrate the Triangle Sum the Triangle Sum Theorem or the Exterior Angle Theorem. Describe procedure. Theorem or Theorem the Exterior Angle Theorem. Describe your procedure. or the Theorem Exterior or Angle the Exterior Theorem. Angle Describe Theorem. your Describe procedure. your procedure. -1Worksheet by Kuta Software LLC CAHlGlA PrCiAgRhatqsv rrxevsve3rRvceOd8.K 5 CMoaBd9e8 5wAiAtghM vIqnEf6i7nNi8tre7 QGYeXoEm9eatyrQyf.Q ©J K2L0H181m eK4uNtUaN 9STo5fBtMwXa2ree9 sLYLRCP.H g CAHlGlA PrCiAgRhatqsv rrxevsve3rRvceOd8.K 5 CMoaBd9e8 5wAiAtghM vIqnEf6i7nNi8tre7 QGYeXoEm9eatyrQyf.Q -1- 4.1 Triangles and Angles 4.1 Triangles and Angles 199 199 Worksheet by Kuta Software LLC ! ()$!!%%%%%%%%%%%%%%%! ! ("$!!%%%%%%%%%%%%%%%! (($!!%%%%%%%%%%%%%%%! 23. An isosceles triangle has ________________________ congruent sides. (*$!!! +,-!%%%%%%%%%%%%%%%! ! 24. An _______________________ triangle has three congruent sides. ! ! ! ! ! ! ! (.$!!!!!!!/,-!%%%%%%%%%%%%%%%! 25. A _________________________ triangle has no congruent sides. 26. If a triangle is isosceles, then is it also equilateral? EXPLAIN your answer. (0$!!!!!!!+/-!%%%%%%%%%%%%%%%! ! ! 2%-0()*+($%0+("+-.)*$(3&(+#4*(),%#-."+1! ! ! !!!(1$! 23!4!%%%%%%%%%%! ! ! ! ! 37!4!%%%%%%%%%%! ! ! ! ! 27!4!%%%%%%%%%%! ! ! ! ! ! ! ! ! ! ! !!!(&$! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !!!(#$!! 56!4!%%%%%%%%%%! ! ! ! 68!4!%%%%%%%%%%! ! ! ! 58!4!%%%%%%%%%%! 9:!4!%%%%%%%%%%! 9;!4!%%%%%%%%%%! :;!4!%%%%%%%%%%!
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