3 Classify Triangles We can classify triangles by the measures of their angles and by the lengths of their sides. Definition Acute Triangle Right Triangle Obtuse Triangle This angle measure is greater than 90°. An acute triangle is one in which all three angles are acute. (All three angles measure less than 90.) A right triangle contains one right, or 90, angle. An obtuse triangle contains one obtuse angle. (The measure of an obtuse angle is greater than 90.) EXAMPLE 5 A right triangle will always have a small square indicating a right angle. Classify each triangle as acute, right, or obtuse. a) A B C b) X Y Z c) P Q R Solution a) This is an obtuse triangle because B is an obtuse angle. 1mB is greater than 90.) b) This is an acute triangle because each angle is acute. (The measure of each angle is less than 90.) c) This is a right triangle because P is a right angle. (mP 90) YOU TRY 5 Classify each triangle as acute, right, or obtuse. a) X Y Z b) P N R c) A B C www.mhhe.com/messersmith SECTION 4.3 Triangles 313
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