4 1 Classifying Triangles Warm Up Lesson Presentation

4 -1 Classifying. Triangles Warm Up Lesson Presentation Lesson Quiz Holt Geometry

4 -1 Classifying Triangles Warm Up Classify each angle as acute, obtuse, or right. 1. 3. right 2. acute obtuse 4. If the perimeter is 47, find x and the lengths of the three sides. x = 5; 8; 16; 23 Holt Geometry

4 -1 Classifying Triangles Objectives Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths. Holt Geometry

4 -1 Classifying Triangles Vocabulary acute triangle equiangular triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle Holt Geometry

4 -1 Classifying Triangles 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. Holt Geometry

4 -1 Classifying Triangles C A B AB, BC, and AC are the sides of A, B, C are the triangle's vertices. Holt Geometry ABC.

4 -1 Classifying Triangles Triangle Classification By Angle Measures Acute Triangle Three acute angles Holt Geometry

4 -1 Classifying Triangles Triangle Classification By Angle Measures Equiangular Triangle Three congruent acute angles Holt Geometry

4 -1 Classifying Triangles Triangle Classification By Angle Measures Right Triangle One right angle Holt Geometry

4 -1 Classifying Triangles Triangle Classification By Angle Measures Obtuse Triangle One obtuse angle Holt Geometry

4 -1 Classifying Triangles Class Example: Classifying Triangles by Angle Measures Classify BDC by its angle measures. B is an obtuse angle. So triangle. Holt Geometry BDC is an obtuse

4 -1 Classifying Triangles Class Example: Classifying Triangles by Angle Measures 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. Holt Geometry

4 -1 Classifying Triangles Example 1 - 3 Classify measure EHG, EFH, Triangle EHG is right Triangle EFH is obtuse Triangle FHG is equiangular Holt Geometry FHG by its angle

4 -1 Classifying Triangles Triangle Classification By Side Lengths Equilateral Triangle Three congruent sides Holt Geometry

4 -1 Classifying Triangles Triangle Classification By Side Lengths Isosceles Triangle At least two congruent sides Holt Geometry

4 -1 Classifying Triangles Triangle Classification By Side Lengths Scalene Triangle No congruent sides Holt Geometry

4 -1 Classifying Triangles Remember! When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent. Holt Geometry

4 -1 Classifying Triangles Class Example: Classifying Triangles by Side Lengths Classify EHF by its side lengths. From the figure, isosceles. Holt Geometry . So HF = 10, and EHF is

4 -1 Classifying Triangles Class Example: Classifying Triangles by Side Lengths Classify EHG by its side lengths. By the Segment Addition Postulate, EG = EF + FG = 10 + 4 = 14. Since no sides are congruent, EHG is scalene. Holt Geometry

4 -1 Classifying Triangles Example # 1 - 3 Classify lengths. ABC, ABD and ABC = equilateral Triangle ABD = Scalene Triangle ACD = scalene Holt Geometry ACD by its side

4 -1 Classifying Triangles Example # 1: Using Triangle Classification Find the side lengths of Step 1 Find the value of x. JK = KL 4 x – 1. 3 = x + 3. 2 3 x = 4. 5 x = 1. 5 Holt Geometry JKL.

4 -1 Classifying Triangles Example #1 Continued Find the side lengths of Step 2 Substitute 1. 5 into the expressions to find the side lengths. JK = 4 x – 1. 3 = 4(1. 5) – 1. 3 = 4. 7 KL = x + 3. 2 = 1(1. 5) + 3. 2 = 4. 7 JL = 5 x + 0. 2 = 5(1. 5) +0. 2 = 7. 3 Holt Geometry JKL.

4 -1 Classifying Triangles Example # 2 Find the side lengths of equilateral FGH. Step 1 Find the value of y. Given. FG = GH = FH Def. of segs. Substitute 3 y – 4 = 2 y + 3 (3 y – 4) for FG and (2 y + 3) for GH. y=7 Holt Geometry Add 4 and subtract 2 y from both sides.

4 -1 Classifying Triangles Check It Out! Example #2 Continued Find the side lengths of equilateral FGH. Step 2 Substitute 7 into the expressions to find the side lengths. FG = 3 y – 4 = 3(7) – 4 = 17 GH = 2 y + 3 = 2(7) + 3 = 17 FH = 5 y – 18 = 5(7) – 18 = 17 Holt Geometry

4 -1 Classifying Triangles Homework: Page 219: # 1 -19 Holt Geometry

4 -1 Classifying Triangles Exit Question Classify each triangle by its angles and sides. 1. MNQ acute; equilateral 2. NQP obtuse; scalene 3. MNP acute; scalene 4. Find the side lengths of the triangle. 29; 23 Holt Geometry

4 -1 Classifying Triangles Exit Question Name: Classify each triangle by its angles and sides. 1. MNQ 2. NQP 3. MNP 4. Find the side lengths of the triangle. Holt Geometry

4 -1 Classifying Triangles Exit Question Name: Classify each triangle by its angles and sides. 1. MNQ 2. NQP 3. MNP 4. Find the side lengths of the triangle. Holt Geometry