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4.1 Triangles and Angles

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Definition of a triangle A triangle is three segments joined at three noncollinear end points.

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Types of Triangles by Sides 3 Sides congruent Equilateral

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Types of Triangles by Sides 2 Sides congruent Isosceles Part of the Isosceles Triangle

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Types of Triangles by Sides No Sides congruent Scalene

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Types of Triangles by Sides 3 Sides congruent Equilateral 2 Sides congruent Isosceles No Sides congruent Scalene

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Types of Triangle by Angles All Angles less than 90 degrees Acute

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Types of Triangle by Angles One Angle greater than 90 degrees, but less than 180° Obtuse

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Types of Triangle by Angles One Angle equal to 90 degrees Right

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How to classify a triangle Choose one from each category Sides Angles____ Scalene Acute Isosceles Right Equilateral Obtuse

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Equiangluar All the angles are Equal This will ALWAYS be paired up with Equilateral

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Parts of the Right Triangle Across from the right angle is the hypotenuse.

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Interior Angles vs. Exterior Angles M a N bc P Interior angles:

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Triangle Sum Theorem The sum of the three interior angles of a triangle is 180º a bc m

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Triangle Sum Theorem Solve for x

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Example 2 Find the measure of each angle. 2x + 10 xx + 2

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Exterior Angle Theorem The measure of an exterior angle equals the measure of the two nonadjecent interior angles.

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Example 3 Given that A is 50º and B is 34º, what is the measure of BCD? What is the measure of ACB? D A B C

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Solve for x

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Corollary for the fact that interior angles add to 180º The acute angles of a Right triangle are complementary.

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Example 4 A. Given the following triangle, what is the length of the hypotenuse? B. What are the length of the legs? C. If one of the acute angle measures is 32°, what is the other acute angles measurement?

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Example 6 Find the missing measures 80° 53°

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Example 7 Given: ABC with m C = 90° Prove: m A + m B = 90° StatementReason 1. m C = 90° 2. m A + m B + m C = 180° 3. m A + m B + 90° = 180° 4. m A + m B = 90°

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