Create Presentation
Download Presentation

Download Presentation
## Karl Robert Jacobs Geo Journal 4

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Parts of a triangle.**• Acute: iswhenthetriangle´sangles are smallerthan 90 degrees. • Obtuse: whenthetriangle´sanglesishigherthan 90 degrees.**Right : iswhen a triangle has anangle of 90 degrees.**• Scalene: Whenallthetriangle´sangles are different. Equilateral . Allsides are equal.**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**E**• Exreriorangles: • The exterior angles are formedbetween a side of thetriangle and a line that pases throuanotherside of thetriangle.**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**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**Usingssspostulate.**A D C B E Ac congruenttoec Cd congruenttocb Ab congruenttoed BythessspostulatetrianglesAbc and EdC are econgruent.**Apcongruenttoec**pdcongruenttopb Ab congruenttoed BythessspostulatetrianglesAbp and Edp are econgruent. bqcongruenttoec pdcongruenttoqb Ab congruenttoeq BythessspostulatetrianglesAbc and Edq are econgruent.**Usingsaspostulate.**• Ab congruenttoeb • <1 congruentto <2 • Cbcongruenttoeb • Bythesaspostulatetriangle ABC and EBD are congruent. A D B E C**Aqcongruenttoeq**• <1 congruentto <2 • Cqcongruenttoeq • BythesaspostulatetriangleAQC and EQD are congruent. • Aqcongruenttozq • <1 congruentto <2 • Cqcongruenttozq • Bythesaspostulatetriangle AQC and ZQD are congruent.**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**<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