Sec 5.4: Classifying Triangles

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Presentation transcript:

Sec 5.4: Classifying Triangles Objectives: • Classify triangles by their sides • Classify triangles by their angles • Triangle Sum Postulate

Concept: Classifying Triangles 2 Ways to Classify Triangles: By the number of congruent sides By the types of angles in the triangle

Classify by Sides

Concept: Equilateral Triangles Equilateral: Equi –– lateral equal sides Any triangle where all 3 sides are equal. Note: If all 3 sides are equal, then all 3 angles are also equal.

Concept: Equilateral Triangles The “tick” marks indicate that the segments are congruent.

Concept: Isosceles Triangle Isosceles: Any triangle with at least two congruent sides. Note: if 2 sides are congruent, then 2 angles are congruent.

Concept: Scalene Triangle Scalene: NO sides are the same length. Note: Each side has a different number of “tick” marks. This means each side is a Different length. Each angle is marked with a different number of arcs. This means that all angles are different.

Concept: Classifying Angles Zero angle: x = 0º Acute angle: 0º < x < 90º Right angle: x = 90º Obtuse angle: 90º < x < 180º Straight angle: 0º < xº < 90º By the types of angles in the triangle

Classify by Angles

Concept: Obtuse Triangle Obtuse: Any triangle with exactly one obtuse angle. Note: It is not possible to have more than one obtuse angle in a triangle.

Concept: Acute Triangle Acute: Any triangle where all three angles are acute.

Concept: Right Triangle Right: Any triangle that has exactly one right angle.

Concept: Triangle Sum Rule The sum of the interior angles of ANY triangle is 180º.

Concept: Application

Concept: Application x = 15 3x + 5x + 5 + 4x – 5 = 180º 1. Set up equation 3x + 5x + 5 + 4x – 5 = 180º 3x + 5x + 5 + 4x – 5 = 180º 2. Combine Like Terms 12x + 0 = 180º 12x = 180º x = 15 3. Divide by 12 12 12

Concept: Application x = 15 A =3x A = 4x – 5 A = 5x + 5 A = 3(15)

Woot! Woot! Concept: Application x = 15 Check: 45º + 80º + 55º = 180º ? Woot! Woot! 125º+ 55º = 180º ? 180º = 180º ?