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Karl Robert Jacobs Geo Journal 4

Karl Robert Jacobs Geo Journal 4

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Karl Robert Jacobs Geo Journal 4

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  1. Karl Robert JacobsGeoJournal 4

  2. Parts of a triangle. • Acute: iswhenthetriangle´sangles are smallerthan 90 degrees. • Obtuse: whenthetriangle´sanglesishigherthan 90 degrees.

  3. Right : iswhen a triangle has anangle of 90 degrees. • Scalene: Whenallthetriangle´sangles are different. Equilateral . Allsides are equal.

  4. Parts of a triangle. • Alltriangleshave 3 angles and 3 sides. • interior angles: A,B,C • Sides:a,b,c A c b B C a

  5. E • Exreriorangles: • The exterior angles are formedbetween a side of thetriangle and a line that pases throuanotherside of thetriangle.

  6. Exterior angletheorem. • Theorem: m<E+m<A=180degrees. • 1 • Findthe m <a • If m<e0120degree • m<e+m<a=180degree • 120 + m<a = 180 • -120 -120 • m<a=60 E A E A

  7. Find m<e if m<a 0 50 degree • Solution.step 1 • m<a + 90 + m<c = 180 • 50 + 90 + m<c =180 • 140 + m<c = 180 • -140 -140 • M<c = 40 • M<c + m<e 0 180 • 40 + m<e= 180 • -40 -40 • m<e 0 140

  8. Usingssspostulate. A D C B E Ac congruenttoec Cd congruenttocb Ab congruenttoed BythessspostulatetrianglesAbc and EdC are econgruent.

  9. Apcongruenttoec pdcongruenttopb Ab congruenttoed BythessspostulatetrianglesAbp and Edp are econgruent. bqcongruenttoec pdcongruenttoqb Ab congruenttoeq BythessspostulatetrianglesAbc and Edq are econgruent.

  10. Usingsaspostulate. • Ab congruenttoeb • <1 congruentto <2 • Cbcongruenttoeb • Bythesaspostulatetriangle ABC and EBD are congruent. A D B E C

  11. Aqcongruenttoeq • <1 congruentto <2 • Cqcongruenttoeq • BythesaspostulatetriangleAQC and EQD are congruent. • Aqcongruenttozq • <1 congruentto <2 • Cqcongruenttozq • Bythesaspostulatetriangle AQC and ZQD are congruent.

  12. Using asa postulate. • <1 congruent <2 • <Abccongruentto < def • <ABC congruentto <DEF • Bythe ASA postultetriangles ABC and DEF are gongruent D A C B F E

  13. <1 congruent <2 • <Abzcongruentto < def • <ABZ congruentto <DEF • Bythe ASA postultetrianglesABZ and DEF are gongruent • <1 congruent <2 • <AQzcongruentto < def • <AQZ congruentto <DEF • Bythe ASA postultetrianglesAQZ and DEF are gongruent