Understanding Different Types of Triangles and Congruence Theorems
This article explores the four primary types of triangles: equilateral, equiangular, isosceles, and scalene, defining their unique properties. It discusses the fundamental components of triangles, including the essential angle and side relationships dictated by the triangle sum theorem, which states that the sum of the interior angles is always 180 degrees. Additionally, it delves into congruence criteria such as CPCT, SSS, SAS, ASA, and AAS, which provide various methods to establish triangle congruence based on sides and angles.
Understanding Different Types of Triangles and Congruence Theorems
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Presentation Transcript
Geo Journal 4 Alejandro Gonzalez 9-4
Different Types of Triangles • Equilateral is a triangle that the sides are all the same. • Equiangular is a triangle that all angles are the same. • Isosceles is a triangle that has only two equal sides. • Scalene is a triangle that has no equal sides.
Equilateral Ex: • Equiangular Ex: • Isosceles Ex: • Scalene Ex:
Parts that compose a Triangle • A triangle is always composed of 3 angles and 3 sides. • The triangle sum theorem says that the 3 angles of the triangle is allays equal to 180.
Exterior angle theorem • 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. 20 20 35 100 80 100 80 100 35 80 80 80
CPCT • CPCT means that if 2 triangles are congruent then all the angles and sides of both the triangles will be equal.
SSS • The Side Side Side postulate states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
SAS • If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. 6 cm 20 20 3 cm 85 90 5 5 5 6 cm 8 cm 6 cm 85 6 cm 90 8 cm 3 cm
ASA • If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
AAS • If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
