Microsoft Windows Help File Content | 1984-07-30 | 10KB | 2 lines
:SB :SH0431a b :SP208008245048245048245048 :SP245008208048208048208048 :SF E. Equality of Angles and Sides. Make sure you know these theorems, definitions and assumptions. NOTE: < = Angle ^ = Degrees 1. Vertical angles are equal. <a = <b :RA :SD :SB :SH1828A B :SH0933C :SP196136252136224072193136 :SF 2. An isosceles triangle has two sides equal in length. The angle between the equal sides is called the vertex angle. The other two angles are called base angles and are equal. If AC = BC, then <A = <B 3. If two angles of a triangle are equal, the sides opposite are equal. If <A = <B, then AC = BC. :RA :SD :SB :SH1531A B :SH0735C :SH14311 :SP190112266112243080217112 :SF 4. An equilateral triangle (ABC) is equiangular, and an equiangular triangle is equilateral. If AB = BC = AC, then <A = <B = <C 5. An exterior angle of a triangle is the sum of the non-adjacent interior angles. <1 = <B + <C :RA :SD :Q :SB :SH0618A B :SH0540D :SH0328C :SH0740E :SP266039112039174024266048 :SF 1. Given: Isosceles {ABC with AC = BC, and <DBE = 20^. Find <C. (a) 20^ (b) 70^ (c) 140^ (d) 160^ (e) 150^ :RCC 1. (c) 140^ Ans. Since <DBE and <B of {ABC are vertical angles, they are equal <B = <DBE = 20^ Since AC = BC the angles opposite them are equal. <A = <B <A + <B + <C = 180^ 20^+ 20^+ <C = 180^ <C = 140^ Ans. :RA :SD :Q :SB :SH1328A B :SH0532C :SH0230D :SP217046196096238096206016 :SF 2. Given: Isosceles {ABC with <ACD = 130^. Find: <B. (a) 50^ (b) 60^ (c) 65^ (d) 130^ (e) 75^ :RCC 2. (c) 65^ Ans. <ACD and <ACB are supplementary <ACD + <ACB = 180^ 130^ + <ACB = 180^ <ACB = 50^ :RA The angles of triangle total 180^ A + <B + <C = 180^ <A + <B + 50^ = 180^ <A + <B = 130^ In the isosceles triangles, <A = <B <B + <B = 130^ <B = 65^ Ans. :RA :SD :Q :SB :SH0435C :SH0928 y :SH1028D A B :SH0729E :SH1236F :SP189071259071241038224071 :SP196056252088252088252088 :SF 3. Given: {ABC is equilateral and <CAF is a right angle. Find: <y. (a) 30^ (b) 60^ (c) 90^ (d) 150^ (e) 45^ :RCA 3. (a) 30^ Ans. Since ABC is equilateral, <CAB = 60^ <BAF = <CAF - <CAB <BAF = 90^ - 60^ = 30^ <y is a vertical angle to <BAF <y = <BAF = 30^ Ans. :RA :SD :Q :SB :SH1032A B :SH0531D C E :SP224072259072241038224072 :SP215039266039266039266039 :SF 4. Given: {ABC with AB = 10in.; <B = 60^; DCE || AB; <DCA = 60^. Find: Length of BC (a) 4" (b) 10" (c) 20" (d) 50" (e) 8" :RCB 4. (b) 10" Ans. <A = <DCA because they are alternate interior angles <A = 60^ <A + <B + <C = 180^ 60^ + 60^+ <C = 180^ <C = 60^ Therefore {ABC is equilateral and BC = AB = 10". Ans. :RA :SD :Q :SB :SP224071259071241038224071 :SP279032259071279071279071 :SH1032A B D :SH0435C E :SF 5. BE||AC, and BE bisects <CBD. Then, (a) AB = AC (b) AB = BC (c) AC = BC (d) AC = BE (e) AB = AC = BC :RCB 5. (b) AB = BC Ans. Since <ACB and <CBE are alternate interior angles, they are equal. The sum of the angles around a point on one side of a straight line is 180^. <CBA + <CBE + <EBD = 180^ <CBE = <EBD <CBA = 180^ - 2 <CBE <CBA = 180^ - 2 <ACB :RA The sum of the angles of a triangle is 180^ <CAB + <ACB + <CBA = 180^ <CAB = 180^ - <ACB - <CBA <CAB = 180^ - <ACB - (180^ - 2<ACB) <CAB = <ACB Since sides opposite equal angles are equal, AB = BC Ans. :SD :ET :ET
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