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5.1 Vocabulary. acute triangle equiangular triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle. auxiliary line corollary interior exterior interior angle exterior angle remote interior angle. C. A.

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## acute triangle equiangular triangle right triangle obtuse triangle equilateral triangle

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**5.1 Vocabulary**acute triangle equiangular triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle auxiliary line corollary interior exterior interior angle exterior angle remote interior angle**C**A AB, BC, and AC are the sides of ABC. B Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths. A, B, C are the triangle's vertices.**Example 1A: Classifying Triangles by Angle Measures**Classify BDC by its angle measures. Classify ABD by its angle measures.**Example 1B: Classifying Triangles by Side Lengths**Classify EHF by its side lengths. Classify EHGby its side lengths.**Quiz**Classify each triangle by its angles and sides. 1. MNQ 2.NQP 3. MNP 4. Find the side lengths of the triangle.**5 - 1**An auxiliary line is a line that is added to a figure to aid in a proof. An auxiliary line used in the Triangle Sum Theorem**118°**Example 2: Application After an accident, the positions of cars are measured by law enforcement to investigate the collision. Use the diagram drawn from the information collected to find mYWZ. Step 1 Find mWXY. mYXZ + mWXY = 180° Lin. Pair Thm. and Add. Post. 62 + mWXY = 180 Substitute 62 for mYXZ. mWXY = 118° Subtract 62 from both sides.**A corollary is a theorem whose proof follows directly from**another theorem. Here are two corollaries to the Triangle Sum Theorem. 5-1-a 5-1-b**Example 3: Finding Angle Measures in Right Triangles**One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle? (answer in terms of “x”)**The interior is the set of all points inside the figure. The**exterior is the set of all points outside the figure. An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side. 4 is an exterior angle. Exterior Interior 3 is an interior angle.**Each exterior angle has two remote interior angles. A remote**interior angle is an interior angle that is not adjacent to the exterior angle. 4 is an exterior angle. The remote interior angles of 4 are 1 and 2. Exterior Interior 3 is an interior angle.**5-2**Example 3: Applying the Exterior Angle Theorem Find mB.**2 3**Lesson Quiz: Part I 1. The measure of one of the acute angles in a right triangle is 56 °. What is the measure of the other acute angle? 2. Find mABD. 3. Find mN and mP.**Lesson Quiz: Part II**4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store? 30°

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