4-1: Classifying Triangles Grade Distribution 1st 2nd 6th 7th A B C D F 100+ No Shows Avg 11/29/2018 12:14 AM 4-1: Classifying Triangles

Classifying Triangles Section 4–1 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us 11/29/2018 12:14 AM 4-1: Classifying Triangles

Triangle Classification Triangles are polygons with three sides. They are classified by their angle measures and side lengths Angle Measure Acute Triangle has three acute angles Equiangular Triangle has three congruent acute angles Right Triangle has one right angle Obtuse Triangle has one obtuse angle Side Lengths Equilateral Triangle has three congruent sides Isosceles Triangle has at least two congruent sides Scalene Triangle has no congruent sides 11/29/2018 12:14 AM 4-1: Classifying Triangles

Classifying Triangles B A C Sides: 𝑨𝑩 , 𝑩𝑪 , and 𝑨𝑪 are the sides of ΔABC A, B, C are the triangle's vertices 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Example 1 Classify ΔFHG by its angle measures and identify the name. 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Your Turn Classify ΔFHE by its angle measures and identify the name. 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Example 2 Draw an isosceles right angle. If a picture is not possible, explain why. 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Example 3 Draw an scalene equiangular. If a picture is not possible, explain why. 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Your Turn Draw an scalene right angle. If a picture is not possible, explain why. 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Example 4 Classify ΔEHF by its side lengths, the length of 𝑯𝑭 and identify the name. 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Example 5 Classify ΔEHG by its side lengths, the length of 𝑯𝑭 and identify the name. 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Your Turn Classify ΔADB by its side lengths, the length of 𝑨𝑪 and identify the name. 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Example 6 Find the side lengths of ΔJKL, identify the type of triangle, and provide a two-column proof 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Example 6 (Proof) Find the side lengths of ΔJKL, identify the type of triangle, and provide a two-column proof Statements Reasons 1) 𝑱𝑲 ≅ 𝑲𝑳 Given 2) JK = KL Definition of Congruency 3) 4x – 10.7 = 2x + 6.3 + 10.7 + 10.7 Substitution 4) 4x = 2x + 17 -2x -2x Addition POE 5) 2x = 17 Subtraction POE 6) x = 8.5 Division POE 7) JK = 4(8.5) - 10.7 = 23.3 KL = 2(8.5) + 6.3 = 23.3 JL = 5(8.5) + 2 = 44.5 Statements Reasons 1) 𝐽𝐾 ≅ 𝐾𝐿 Given 2) JK = KL Definition of Congruency 3) 4x – 10.7 = 2x + 6.3 + 10.7 + 10.7 Substitution 4) 4x = 2x + 17 -2x -2x Addition POE 5) 2x = 17 Subtraction POE Statements Reasons 1) 𝐽𝐾 ≅ 𝐾𝐿 Given 2) JK = KL Definition of Congruency 3) 4x – 10.7 = 2x + 6.3 + 10.7 + 10.7 Substitution 4) 4x = 2x + 17 -2x -2x Addition POE 5) 2x = 17 Subtraction POE 6) x = 8.5 Division POE Statements Reasons 1) 𝐽𝐾 ≅ 𝐾𝐿 Given 2) JK = KL Definition of Congruency 3) 4x – 10.7 = 2x + 6.3 + 10.7 + 10.7 Substitution 4) 4x = 2x + 17 -2x -2x Addition POE Statements Reasons 1) 𝐽𝐾 ≅ 𝐾𝐿 Given 2) JK = KL Definition of Congruency 3) 4x – 10.7 = 2x + 6.3 + 10.7 + 10.7 Substitution 4) 4x = 2x + 17 -2x -2x Addition POE 5) 2x = 17 Subtraction POE Statements Reasons 1) 𝐽𝐾 ≅ 𝐾𝐿 Given 2) JK = KL Definition of Congruency Statements Reasons 1) 𝐽𝐾 ≅ 𝐾𝐿 Given 2) JK = KL Definition of Congruency 3) 4x – 10.7 = 2x + 6.3 + 10.7 + 10.7 Substitution Statements Reasons 1) 𝐽𝐾 ≅ 𝐾𝐿 Given 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Your Turn Find the side lengths of equilateral ΔFGH and provide a two-column proof Statements Reasons 1) 𝑭𝑮 ≅ 𝑮𝑯 ≅ 𝑭𝑯 Given 2) FG = GH = FH Definition of Congruency 3) FG = GH 4) 3y – 4 = 2y + 3 +4 +4 Substitution 5) 3y = 2y + 7 -2y -2y Addition POE 6) y = 7 Subtraction POE 7) FG = 3(7) – 4 = 17 GH = 2(7) + 3 = 17 FH = 5(7) – 18 = 17 11/29/2018 12:14 AM 4-1: Classifying Triangles

4-1: Classifying Triangles Assignment Page 216 12-19, 21-32 all, 35-37 11/29/2018 12:14 AM 4-1: Classifying Triangles