Types of Triangles And Angle Sum Theorems.  Notation for sides.  AB CB AC  Angles   ABC or  B  Vertex angle  Base angle  Opposite side  Opposite.

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Presentation transcript:

Types of Triangles And Angle Sum Theorems

 Notation for sides.  AB CB AC  Angles   ABC or  B  Vertex angle  Base angle  Opposite side  Opposite angle A B C

 Equilateral Triangle : all sides and angles are congruent. ( Equiangular Triangle) 9 9 9

 At least two sides and two angles are congruent Vertex Base Angles

 None of the sides or angles are congruent

 m∠A + m∠B + m∠C = 180 degrees A B C

 Find the value of the unknown angle. 87 ° 44 ° x° 180 ° – 87 ° – 44 ° =Unknown angle X = 49 ° X° + 87° + 44° = 180°

 m∠ A = (2x – 3)°, m∠ B = (x + 5)°, and m∠ C = (x + 8)° C B A Solution

 m∠A + m∠B = m∠E  The sum of the remote interior angles equal the value of the exterior angle. A B E exterior angle remote interior angle

56° 88° E° 56° + 88° = the unknown exterior angle = 144 degrees

 All angles are congruent. They are each 60 degrees. (Equilateral Triangle) 60°

61° 38° X° Y° Z° 26° 180° – 38° – 61° = 81°  X° 61° + 38° = 99°  Y° 180° – 26° – 99° = 55°  Z°

122 ° 18 ° T° V° K° R° Solution P°