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Geometry Journal 4

Geometry Journal 4. Andres Cofi ño. Types of Triangles. Equiangular: is a triangle that all angles in it have the same measure Equilateral: is a triangle that all sides of it have the same measure Scalene: is a triangle that have no equal sides nor angles

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Geometry Journal 4

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  1. Geometry Journal 4 Andres Cofiño

  2. Types of Triangles • Equiangular: is a triangle that all angles in it have the same measure • Equilateral: is a triangle that all sides of it have the same measure • Scalene: is a triangle that have no equal sides nor angles • Isosceles: is a triangle that two of its sides are congruent to each other

  3. Right triangle: is a triangle that has one angle that its measure is 90 degrees • Obtuse triangle: is a triangle that has one angle that its measure is greater then 90 degrees. Triangles are classified either by its angles or sides, although they can be classified by both (sides and angles).

  4. Obtuse triangle Right triangle Equilateral triangle Isosceles triangle Scalene Triangle

  5. Parts of Triangle • Triangles consist in three angles and three sides. “tri” = three angles • Triangle Sum Theorem says that the sum of the three angles of a triangle equals 180 degrees.

  6. Examples 60^ 60+60+60=180 120^ 60^ 60^ 34^ 26^ 120+34+26=180 80^ 40^ 60^ 80+60+40=180

  7. Exterior Angle Theorem • Says that any exterior angle of a triangle is always equal to the sum of the two non-adjacent sides. 50^ 40^ 80^ 50^ 100^ 40^ 100^ 80^

  8. 60^ 120^ 60^ Exterior Angle Theorem can be used to measure a table or any other triangular/rectangular object.

  9. CPCT • Congruence for shapes consist of having same exact measures of angles and sides. • CPCT- Corresponding Parts of Congruent Triangles is when you have proved two triangles are congruent so each part of one triangle (either side or angle) is congruent to the same side or angle of the other triangle.

  10. B A 5 5 7 5 C B 7 A C 5 5 6 4 4 6 S 5 W W Q S Q

  11. SSS • Side Side Side postulate says that if three sides of a triangle are congruent to three sides of another triangle, then these two triangles are congruent. 5 E QE congr. JL QW congr. JK WE congr. KL 5 5 5 5 J Q 5 K L 2 3 2 1 3 W WQE congruent KJL 1

  12. SAS • Side Angle Side postulate says that if two sides and included angle of a triangle are congruent to two sides and the included angle of another triangle, then those triangles are congruent. 3 90^ 8 10 45^ 5 5 60^ 10 4 5 4 60^ 45^ 5 90^ 8 3

  13. ASA • The Angle Side Angle postulate says that if two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then both triangles are congruent. 8 90^ 45^ 90^ 30^ 9 9 70^ 30^ 90^ 70^ 70^ 70^ 4 90^ 45^ 4 8

  14. AAS • The Angle Angle Side postulate says that if two angles and the non-included side of a triangle are congruent to two angles and the non-included angle of another triangle, then these two triangles are congruent. 45^ 90^ 11 60^ 7 7 60^ 11 60^ 60^ 90^ 45^

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