4-2 Identifying Triangles Chapter 4 4-2 Identifying Triangles

Objectives Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths.

What is triangle? a triangle ( ∆) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths.

Classifying triangles by angles Acute triangle : three acute angles Equiangular triangle: Three congruent angles Right triangle: One right angle

Classifying triangles by angles Obtuse triangle: One obtuse triangle

Example Classify ∆ BDC by its angle measures B is an obtuse angle. B is an obtuse angle. So BDC is an obtuse triangle.

Example 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.

Student Guided Practice Do problems 3-5 in your book page 227

Classifying triangles by sides Equilateral triangle: Three congruent sides Isosceles triangle: Two congruent sides Scalene: No congruent sides

Example Classify ∆ EHF by its side lengths. From the figure, . So HF = 10, and EHF is isosceles.

Example Classify ∆ ACD by its side lengths. From the figure, . So AC = 15, and ACD is scalene.

Example Find the side lengths of ∆ JKL.

Example Find the side lengths of equilateral ∆ FGH.

Student Guided practice Do problems 9 and 10

Application 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?

Closure Today we learned about classifying triangles and solving problems involving triangles Next class we are going to learn about finding the measure of the interior and exterior angles of a triangle.