Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3. 4. If the perimeter is 47, find x and the lengths of the three sides. right acute x =

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Presentation transcript:

Warm Up Classify each angle as acute, obtuse, or right If the perimeter is 47, find x and the lengths of the three sides. right acute x = 5; 8; 16; 23 obtuse

B A C AB, BC, and AC are the sides of ABC. A, B, C are the triangle's vertices. 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.

Triangles Classified by ANGLE MEASURES Three acute angles Acute Equiangular Three congruent acute angles Right One right angle Obtuse One obtuse angle

Classify BDC by its angle measures. Example 1: B is an obtuse angle. B is an obtuse angle. So BDC is an obtuse triangle. Classify ABD by its angle measures. ABD and CBD form a linear pair, so they are supplementary. Therefore mABD + mCBD = 180°. By substitution, mABD + 100° = 180°. So mABD = 80°. ABD is an acute triangle by definition.

Triangles Classified by SIDE LENGTHS Equilateral Three congruent sides Isosceles At least two congruent sides ScaleneNo congruent sides

Remember! When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent. Classify EHF by its side lengths. Example 2: From the figure,. So HF = 10, and EHF is isosceles. Classify EHG by its side lengths. By the Segment Addition Postulate, EG = EF + FG = = 14. Since no sides are congruent, EHG is scalene.

Example 3: Find the side lengths of JKL. JK = KL 4x – 10.7 = 2x x = 17.0 x = 8.5 JK = 4x – 10.7 = 4(8.5) – 10.7 = 23.3 KL = 2x = 2(8.5) = 23.3 JL = 5x + 2 = 5(8.5) + 2 = 44.5

The amount of steel needed to make one triangle is equal to the perimeter P of the equilateral triangle. P = 3(18) P = 54 ft A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the triangle is 18 feet long. How many triangles can be formed from 420 feet of steel beam? Example 4: 420  54 = 7 triangles 7979 There is not enough steel to complete an eighth triangle. So the steel mill can make 7 triangles from a 420 ft. piece of steel beam.