Chapter 4.1 Notes: Apply Triangle Sum Properties

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Presentation transcript:

Chapter 4.1 Notes: Apply Triangle Sum Properties Goal: You will classify triangles and find measures of their angles.

Classification By Sides Classification By Angles

Classifying Triangles In classifying triangles, be as specific as possible. Obtuse, Isosceles Acute, Scalene

Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180o. 3 2 1 m<1 + m<2 + m<3 = 180°

60º 90º 30º 60º 180º 30º 90º Property of triangles The sum of all the angles equals 180º degrees. 60º 90º 30º + 60º 180º 30º 90º

40º 90º 40º 50º 180º 50º 90º Property of triangles The sum of all the angles equals 180º degrees. 40º 90º 40º 50º + 180º 50º 90º

60º 60º 60º 180º Property of triangles 60º 60º 60º The sum of all the angles equals 180º degrees. 60º 60º 60º 60º + 180º 60º 60º

What is the missing angle? 70º 70º ? ? + 180º 70º 70º 180 – 140 = 40˚

What is the missing angle? 90º ? 30º ? + 30º 90º 180º 180 – 120 = 60˚

What is the missing angle? 60º 60º ? + 60º 60º 180º 180-120 = 6060˚

What is the missing angle? 30º 78º ? + 78º 30º 180º 180 – 108 = 72˚

Find all the angle measures 45x 10x 35x 180 = 35x + 45x + 10x 180 = 90x 2 = x 90°, 70°, 20°

Ex.2: Classify the triangle shown in the diagram by its sides and angles.

Ex.3: Classify the triangle by its sides and angles.

Angles When the sides of a polygon are extended, other angles are formed. The original angles are the interior angles. The angles that form linear pairs with the interior angles are the exterior angles.

Theorem 4.2 Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Ex.4: Find . Ex.5: Find the measure of in the diagram shown.

A corollary to a theorem is a statement that can be proved easily using the theorem. Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are complementary.

Ex. 6: The tiled staircase shown forms a right triangle Ex.6: The tiled staircase shown forms a right triangle. The measure of one acute angle in the triangle is twice the measure of the other. Find the measure of each acute angle.

Ex.7: Find Ex.8: Find the measure of each interior angle of ∆ABC, where

Ex.9: Find the measures of the acute angles of the right triangle in the diagram shown.