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Karl Robert Jacobs Geo Journal 4. Parts of a triangle . Acute : is when the triangle´s angles are smaller than 90 degrees . Obtuse : when the triangle´s angles is higher than 90 degrees . Right : is when a triangle has an angle of 90 degrees .
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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