5 1 Types of Triangles Angles of Triangles

5. 1 Types of Triangles & Angles of Triangles

Given ΔPQR: a. Which angle is opposite segment PQ? b. Which side is opposite angle Q? c. Which side is included between angle P and angle R? d. Which angle is included between segments QR and PR? Identifying Parts of a Triangle Copyright © 2014 Pearson Education, Inc.

Type Description Scalene No sides are equal Isosceles At least 2 sides are equal Example Equilateral All. Triangles sides are by Angles Classifying and Sides. equal Copyright © 2014 Pearson Education, Inc.

Type Description Acute All (3) acute angles 1 obtuse angle Obtuse Example Equiangula All angles are r equal. Classifying Triangles by Angles Right 1 right angles and Sides. Copyright © 2014 Pearson Education, Inc.

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Find the measure of the exterior angle and the nonadjacent angle shown. Solution 3 x – 53 = x + 67 2 x – 3 = 67 2 x = 120 x = 60 Finding Angle Measures Copyright © 2014 Pearson Education, Inc.

The two acute angles of a right triangle are complementary. m∠ 1 + m∠ 2 = 90° Acute Angles of a Right Triangle Copyright © 2014 Pearson Education, Inc.

If an isosceles triangle has exactly two congruent (equal measure) sides, then these two sides are its legs. The third side is the base. The angle opposite the base is the vertex angle. The other two angles adjacent to the base are the base angles. Definitions Copyright © 2014 Pearson Education, Inc.

Isosceles Triangle Theorem Copyright © 2014 Pearson Education, Inc.

C is the longest side of the triangle! Right Triangle Obtuse Triangle Acute Triangle Extensions of Pythagorean Theorem