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Transcript
JOURNAL TRIANGLEs Mateo Safie Types of Triangles • Equilateral: a triangle whose sides are all the same. • Equiangular: a triangle which all angles are the same. • Isosceles: a triangle that only has two equal sides • Scalene: a triangle that has no equal side PARTS OF A TRIANGLE • A triangle is formed out of thee sides and tree angles. • The triangle sum Thm. states that the sum of all the angles has to be equal to 180 degree. EXTERIOR ANGLES • The exterior angle Thm. States that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle and the exterior angle is supplementary tor the adjacent angle. Exterior angles ex: 37.5 37.5 40 75 105 80 40 40 40 80 CPCT • Congruence in complete shapes is more complex because all of the sides and angles have to be in the same side. • CPCT means that once we know that two triangles are congruent, we know that all corresponding sides and angles are congruent! CPCT ex: <ABC is not = to <BAC 4cm 1cm 1cm 3 cm 4cm 3 cm 4cm 4cm 4cm 4cm 4cm 4cm SSS • The side side side postulate states that if all sides from one triangle are equal to all sides from other triangle, then the triangles are congruent. SSS ex: 7cm 5cm 5cm 7cm 4cm 4cm 1cm 4cm 3cm 5cm 4cm 3cm 1cm 3cm 1cm 3cm 1cm SAS • The side angle side postulate states that if two sides and one angle are equal to two sides and one angle from another triangle, then both triangles are congruent SAS ex: 85 3cm 85 3cm 5cm 6cm 35 90 5cm 90 35 6cm 6cm ASA, AAS • ASA and AAS postulates state that if two angles and one side are equal to other two angles an ones side, both of the triangles are congruent. ASA ex: 75 75 6cm 6cm 55 20 40 85 4cm 55 25 40 25 85 20 AAS ex: 7cm 7cm 75 55 75 55 20 40 40 25 85 4cm 25 85 4cm 20