Multimedia Geometry

home *** CD-ROM | disk | FTP | other *** search

/ Multimedia Geometry / geometry-3.5.iso / GEOMETRY / CHAPTER3.1Y < prev next >

Wrap

Text File | 1995-04-22 | 8KB | 291 lines

à 3.1èTriangle Defïitions äèPlease answer ê followïg questions about triangles. â èèèèèèèè A triangle is ê union ç three segmentsè èèèèèèèè joïïg three noncollïear poïts. éS1 Probably ê most important geometric figure is ê triangle. Defïition 3.1.1èTRIANGLE:èA triangle is ê union ç three segments joïïg three noncollïear poïts. è Every triangle has three sides å three angles.èSome triangles are identified by ê type ç angles êy have.èFor example, certaï tri- angles are called acute, obtuse, right, or equiangular.èOêr triangles are identified by ê lengths ç êir sides.èFor example, certaï tri- angles are called scalene, isosceles, or equilateral. Defïition 3.1.2èACUTE TRIANGLE:èAn acute triangle is one ï which all angles are acute angles. Defïition 3.1.3èOBTUSE TRIANGLE:èAn obtuse triangle is a triangleè with one obtuse angle. Defïition 3.1.4èRIGHT TRIANGLE:èA right triangle is a triangle with one right angle.èIn a right triangle ê longest side is called ê hypotenuse, å ê oêr two sides are called ê legs ç ê triangle. Defïition 3.1.5èEQUIANGULAR TRIANGLE:èAn equiangular triangle is a triangle with all angles equal. Defïition 3.1.6èSCALENE TRIANGLE:èA scalene triangle is a triangle with no two sides congruent. Defïition 3.1.7èISOSCELESE TRIANGLE:èAn isosceles triangle is a tri- angle with two equal sides.èThe third side is called ê base. Defïition 3.1.8èEQUILATERAL TRIANGLE:èA triangle is an equilateral triangle if all three sides are equal ï length. èèèèèèèèèèèèèèèèèèèè This figure shows ΦABC.èThis èèèèèèèèèèèèèèèèèèèè triangle has three sides å èèèèèèèèèèèèèèèèèèèè three angles, ▒┤, ┤╖, ╖▒, ╬A, èèèèèèèèèèèèèèèèèèèè ╬B, å ╬C.èIn this figure èèèèèèèèèèèèèèèèèèèè we would say that ╬A is oppo- èèèèèèèèèèèèèèèèèèèè site side ┤╖, ╬B is oppositeè @fig3101.BMP,35,220,147,74èèèèèèè side ▒╖, å ╬C is opposite side ▒┤.èAlso, we would say that ╬A is ïcluded by sides ▒┤ å ▒╖, å side ▒┤ is ïcluded by ╬A å ╬B.èWe would refer ë A, B, å C as ê vertices.èWe would also say that x is ïterior å y is exterior ë ê triangle. è Some triangles can be described by more han one term.èFor example, a right triangle with all sides ç different lengths could be called a right, scalene triangle.èA right triangle with two equal sides could be called an isosceles, right triangle.èOêr examples are equilateral, acute triangle å isosceles, obtuse triangle. 1èèèèè What kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèA) Isosceles, right triangle èèèèèèèèèèèèèèèèèèèèèèB) Scalene, right triangle èèèèèèèèèèèèèèèèèèèèèèC) Obtuse, right triangle èèèèèèèèèèèèèèèèèèèèèèD) None @fig3102.BMP,35,40,147,74è ü èèèèèèèèè ΦABC is a scalene, right triangle. Ç Bèèèèè 2èèèèèè Name ê hypotenuse ç ΦABC.è èèèèèèèèèèèèèèèèèèèèèèèèèèèèèA) ▒┤ èèèèèèèèèèèèèèèèèèèèèèèèèèèèèB) ▒╖ èèèèèèèèèèèèèèèèèèèèèèèèèèèèèC) ┤╖ èèèèèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3102.BMP,35,40,147,74è ü èèèèèèèèèèèèThe hypotenuse is side ▒┤. Ç Aè 3èèèèèèèèè Name ê legs ç ΦABC. èèèèèèèèèèèèèèèèèA)èa å c èèèèèèèèèèèèèèèèèB)èc å b èèèèèèèèèèèèèèèèèC)èb å a èèèèèèèèèèèèèèèèèD)èNone ç êse @fig3102.bmp,35,40,147,74èèèè ü èèèèèèèèèèThe legs are sides a å b. Ç C 4èèèèèèWhat kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèèèè A) Obtuse triangleè èèèèèèèèèèèèèèèèèèèèèèèèè B) Scalene triangle èèèèèèèèèèèèèèèèèèèèèèèèè C) Isosceles triangle èèèèèèèèèèèèèèèèèèèèèèèèè D) None @fig3103.BMP,35,40,147,74è ü èèèèèèèèèè ΦABC is an isosceles triangle. Ç Cèèèèè 5èèèèèèName ê vertex angle ç ΦABC.è èèèèèèèèèèèèèèèèèèèèèèèèèèèèA) ╬Aè èèèèèèèèèèèèèèèèèèèèèèèèèèèèB) ╬B èèèèèèèèèèèèèèèèèèèèèèèèèèèèC) ╬C èèèèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3103.BMP,35,40,147,74è ü èèèèèèèThe vertex angle ç an isosceles triangle is êè èèèèèèèangle ïcluded by ê two equal sides.è╬Aèè Ç Aèèèèè 6èèèèèèName ê base angles ç ΦABC.è èèèèèèèèèèèèèèèèèèèèèèèèèèèèA) ╬A å ╬Bè èèèèèèèèèèèèèèèèèèèèèèèèèèèèB) ╬B å ╬C èèèèèèèèèèèèèèèèèèèèèèèèèèèèC) ╬A å ╬C èèèèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3103.BMP,35,40,147,74è ü èèèèèèèèèè The base angles are ╬B å ╬C.è èèèèèèè Ç Bèèèèè 7èèèèèèèèName ê legs ç ΦABC.è èèèèèèèèèèèèèèèèèèèèèèèèèèèèèA) a å cè èèèèèèèèèèèèèèèèèèèèèèèèèèèèèB) b å a èèèèèèèèèèèèèèèèèèèèèèèèèèèèèC) b å c èèèèèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3103.BMP,35,40,147,74è ü èèè The legs ç an isosceles triangle are ê two equal sides.èèèèèèèè Ç Cèèèèè 8èèèèè What kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèèè A) Equilateral triangleèè èèèèèèèèèèèèèèèèèèèèèèèè B) Scalene triangle èèèèèèèèèèèèèèèèèèèèèèèè C) Obtuse triangle èèèèèèèèèèèèèèèèèèèèèèèè D) None @fig3104.BMP,35,40,147,74è ü èèèèèèèèèè ΦABC is an equilateral triangle.èèèèèèèè Ç A 9èèèèèèWhat kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèèèèè A) Right triangleèè èèèèèèèèèèèèèèèèèèèèèèèèèè B) Obtuse triangle èèèèèèèèèèèèèèèèèèèèèèèèèè C) Acute triangle èèèèèèèèèèèèèèèèèèèèèèèèèè D) None @fig3104.BMP,35,40,147,74è ü èèèèèèèèèèèèΦABC is an acute triangle.èèèèèèèè Ç Cèèèèè 10èèèèèèWhat kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèèè A) Scalene triangleèè èèèèèèèèèèèèèèèèèèèèèèèè B) Equiangular triangle èèèèèèèèèèèèèèèèèèèèèèèè C) Right triangle èèèèèèèèèèèèèèèèèèèèèèèè D) None @fig3104.BMP,35,40,147,74è ü èèèèèèèèèè ΦABC is an equiangular triangle.èèèèèèèè Ç Bèèèèè 11èèèèèèWhat kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèèè A) Isosceles triangleèè èèèèèèèèèèèèèèèèèèèèèèèè B) Scalene triangle èèèèèèèèèèèèèèèèèèèèèèèè C) Acute triangle èèèèèèèèèèèèèèèèèèèèèèèè D) None @fig3105.BMP,35,40,147,74è ü èèèèèèèèèèèΦABC is an isosceles triangle.èèèèèèèè Ç Aèèèèè 12èèèèèèWhat kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèèè A) Acute triangleèè èèèèèèèèèèèèèèèèèèèèèèèè B) Right triangle èèèèèèèèèèèèèèèèèèèèèèèè C) Obtuse triangle èèèèèèèèèèèèèèèèèèèèèèèè D) None @fig3105.BMP,35,40,147,74è ü èèèèèèèèèèèèΦABC is an obtuse triangle.èèèèèèèè Ç Cèèèèè 13èèèèèèWhat kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèèè A) Scalene triangleèè èèèèèèèèèèèèèèèèèèèèèèèè B) Acute triangle èèèèèèèèèèèèèèèèèèèèèèèè C) Isosceles triangle èèèèèèèèèèèèèèèèèèèèèèèè D) None @fig3102.BMP,35,40,147,74è ü èèèèèèèèèèè ΦABC is a scalene triangle.èèèèèèèè Ç Aèèèèè 14èèèèèèWhat kïd ç triangle is ΦABC?è èèèèèèèèèèèèèèèèèèèèèèèèèèA) Obtuse triangleèè èèèèèèèèèèèèèèèèèèèèèèèèèèB) Right triangle èèèèèèèèèèèèèèèèèèèèèèèèèèC) Acute triangle èèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3102.BMP,35,40,147,74è ü èèèèèèèèèèèè ΦABC is a right triangle.èèèèèèèè Ç Bèèèèè 15èèèWhat kïd ç triangle is ΦABC?è a ƒ b ƒ cè èèèèèèèèèèèèèèèèèèèA) Right, obtuse triangleèè èèèèèèèèèèèèèèèèèèèB) Acute, scalene triangle èèèèèèèèèèèèèèèèèèèC) Isosceles, equilateral triangle èèèèèèèèèèèèèèèèèèèD) None @fig3106.BMP,35,40,147,74è ü èèèèèèèèè ΦABC is an acute, scalene triangle.èèèèèèèè Ç Bèèèèè 16èèèèè What side is ïcluded by ╬A å ╬C?è èèèèèèèèèèèèèèèèèèèèèèèèèèèèèA) ┤╖èè èèèèèèèèèèèèèèèèèèèèèèèèèèèèèB) ▒╖ èèèèèèèèèèèèèèèèèèèèèèèèèèèèèC) ▒┤ èèèèèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3106.BMP,35,40,147,74è ü èèèèèèèèèè Side ▒╖ is ïcluded by ╬A å ╬C.èèèèèèèèèèèèèèèèè Ç Bèèèèè 17èèèè What angle is ïcluded by ▒┤ å ┤╖?è èèèèèèèèèèèèèèèèèèèèèèèèèèèèèA) ╬Bèè èèèèèèèèèèèèèèèèèèèèèèèèèèèèèB) ╬C èèèèèèèèèèèèèèèèèèèèèèèèèèèèèC) ╬A èèèèèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3106.BMP,35,40,147,74è ü èèèèèèèèèèè╬B is ïcluded by ▒┤ å ┤╖.èèèèèèèèèèèèèèèèè Ç Aèèèèè 18èèèèèèè What side is opposite ╬C?è èèèèèèèèèèèèèèèèèèèèèèèèèèèèèèA) ▒╖èè èèèèèèèèèèèèèèèèèèèèèèèèèèèèèèB) ┤╖ èèèèèèèèèèèèèèèèèèèèèèèèèèèèèèC) ▒┤ èèèèèèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3106.BMP,35,40,147,74è ü èèèèèèèèèèèèèSide ▒┤ is opposite ╬C.èèèèèèèèèèèèèèèèè Ç Cèèèèè 19èèèèèèWhat angle is opposite side ┤╖?è èèèèèèèèèèèèèèèèèèèèèèèèèèèèèèA) ╬Bèè èèèèèèèèèèèèèèèèèèèèèèèèèèèèèèB) ╬A èèèèèèèèèèèèèèèèèèèèèèèèèèèèèèC) ╬C èèèèèèèèèèèèèèèèèèèèèèèèèèèèèèD) None @fig3106.BMP,35,40,147,74è ü èèèèèèèèèèèè ╬A is opposite side ┤╖.èèèèèèèèèèèèèèèèè Ç Bèèèèè