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Understanding the Parts and Types of Triangles

This guide explores the various types of triangles, including acute, obtuse, right, scalene, and equilateral triangles. Each type is defined based on the measure of its angles and the equality of its sides. The guide also covers the exterior angle theorem and provides problem-solving examples to find unknown angles using triangle properties and congruence postulates (SSS, SAS, ASA). Triangles always consist of three sides and three angles, forming the basis of their classification.

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Understanding the Parts and Types of Triangles

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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

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