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Geometry Journal Chapter 4

Geometry Journal Chapter 4. JOSE ANTONIO WEYMANN 9-3. M2 GEOMETRY/ALGEBRA. TRIANGLES. *Equilateral *Isosceles *Scalene Right Acute Obtuse Equiangular. Triangle types:. Equilateral: Is a triangle with three congruent sides.

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Geometry Journal Chapter 4

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  1. Geometry Journal Chapter 4 JOSE ANTONIO WEYMANN 9-3 M2 GEOMETRY/ALGEBRA

  2. TRIANGLES *Equilateral *Isosceles *Scalene Right Acute Obtuse Equiangular

  3. Triangle types: • Equilateral: Is a triangle with three congruent sides. • Isosceles: Is a triangle with at least two congruent sides. • Scalene: Is a triangle with no congruent sides

  4. Triangle types: • Equiangular: A triangle with three congruent angles. • Acute: A triangle with three acute angles. • Right: A triangle with one right angle. • Obtuse: A triangle

  5. Triangle Types • We use the different classifications into categories by: we combine the terms of the first slide with the ones of the second slide. We need to know the different types for next lessons and chapters. In real life we could use them for construction to know that amount of material needed in triangular shapes. • Example: Obtuse Isosceles

  6. Parts of a triangle: • Sides: are the segments that make the three sided figure • Verteces: are the points at which the sides meet • Triangle Sum Theorem: The sum of the angle measures of triangle are 180º 45º ^1= 180º ^2= 180º 90º 45º 1 2

  7. Parts of a triangle: • Exterior angle: is an angle formed from one side of the triangle and the extension in the adjacent part of the side. < 1 <2 • Interior angle: is an angle formed by two sides 2 3 1

  8. r Exterior Angle Theorem • m<4 = m<1 + m<2 • We use this theorem to find the measures vertices we don’t know in a triangle with a exterior angle, in real life we could use this in construction to know the necessary angle for support in triangular shape bases. • Examples: <4= 180ª m<1 +m<2= 180º

  9. Exterior Angle Theorem • Examples: 55º <X m<X= 110º 55º 34º 80º <Y m<Y= 114º

  10. Congruence in shapes & CPCT • Shapes are congruent if they have the same measure; if they are being stated as congruent the vertices have to be in the same order; they have to have same size, shape, and position. • CPCT : Corresponding Parts of Congruent Triangles (e.g.) A B C D AB = 4ft. 4ft.

  11. Congruence in shapes & CPCT • (e.g.) # 2 E G EF congruent to GH F H • (e.g.) # 3 M W2

  12. SSS • SIDE-SIDE-SIDE: this postulate says if two triangles have there three sides congruent to one another, then the triangle themselves are congruent. 4cm. 4cm. 4cm. 4cm. 4cm. 4cm.

  13. SSS 2ft. 2ft. 4ft. 2ft. 2ft. 4ft. Both triangles are congruent because of Side-Side-Side

  14. SAS • SIDE-ANGLE-ANGLE: this postulate says that if the sides and included angle in two triangles are congruent, then the triangles are congruent.

  15. SAS

  16. ASA • ANGLE-SIDE-ANGLE: this postulate says that if the two angles and the included side of two triangles are congruent, then the triangles are congruent themselves.

  17. ASA ^1 congruent to ^2 1 2

  18. AAS • ANGLE-ANGLE-SIDE: this postulate says that if two triangles have their two angles and included side are congruent, then the triangles are congruent.

  19. AAS

  20. AAS • The triangles are congruent because of Angle-Angle-Side

  21. Conclusion • I hope to have covered the topics appropriately, and I believe I am ready for the exam.

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