Triangles 1 The Basics. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB∆CBA∆BCA.

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Presentation transcript:

Triangles 1 The Basics

2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB∆CBA∆BCA ∆ACB A B C

3 Opposite Sides and Angles Opposite Sides: Side opposite to angle A Side opposite to angle B Side opposite to angle C Opposite Angles: Angle opposite to : angle A Angle opposite to : angle B Angle opposite to : angle C

Classifying Triangles by Sides Equilateral: 4 Scalene: A triangle in which all 3 sides are different lengths. Isosceles: A triangle in which at least 2 sides are equal. A triangle in which all 3 sides are equal. 3.2 cm 3.15 cm C 3.55 cm A B C 3.47 cm 5.16 cm B C A G H I 3.7 cm

Classifying Triangles by Angles A triangle in which all 3 angles are less than 90˚. 5 Acute: Obtuse: A triangle in which one and only one angle is greater than 90˚& less than 180˚ 108 ° 44 ° 28 ° B C A 57 ° 47 ° 76 ° G HI

Classifying Triangles by Angles 6 Right: Equiangular: A triangle in which one and only one angle is 90˚ A triangle in which all 3 angles are the same measure.

7 polygons Classification by Sides with Flow Charts & Venn Diagrams triangles Scalene Equilateral Isosceles Triangle Polygon scalene isosceles equilateral

8 polygons Classification by Angles with Flow Charts & Venn Diagrams triangles Right Equiangular Acute Triangle Polygon right acute equiangular Obtuse obtuse

9 Theorems & Corollaries The sum of the interior angles in a triangle is 180˚. Triangle Sum Theorem: Third Angle Theorem: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Corollary 1: Each angle in an equiangular triangle is 60˚. Corollary 2:Acute angles in a right triangle are complementary. Corollary 3: There can be at most one right or obtuse angle in a triangle.

10 Exterior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Exterior Angle Remote Interior Angles A B C D Example:Solve for x. 3x - 22 = x x – x = x = 102 m<A = x = 51°

Classifying Triangles There are 3 ways to classify a triangle by its sides. Scalene Isosceles Equilateral There are 4 ways to classify a triangle by its angles. Acute Right Obtuse Equiangular ** Equiangular Triangles are always Equilateral.