1. Honors Geometry Unit 4.1 By: Destiny Moon and Katja Ziemer

2. TRIANGLES CAN BE CLASSIFIED TWO DIFFERENT WAYS 1.By side lengths 2. By angle measures

3. 1.Classifying triangles by side lengths Scalene: no congruent sides Isosceles: at least 2 sides are congruent Equilateral: all sides are congruent

4. 2. Classifying triangles by angle measures Acute: all angles are acute Equiangular: all angles are acute and congruent (each angle is 60 degrees) Obtuse: one obtuse, and two acute angles Right: one right angle, two acute angles (add up to 90 degrees )

5. Sample Problems : Triangle DES is an equilateral triangle with DE= x+3, ES=3x-3, and SD= 2x. Find the length of each side. D E S x+3 3x-3 2x DE= x+3 3+3 6 ES= 3x-3 3(3)-3 9-3 6 SD=2x 2(3) 6 2x = x+3 -x x = 3

6. Sample Problems: Triangle KAT is an isosceles triangle, with KA=4x+2, AT=5x, and TK=3+1. The base is line segment TK. Find the length of each side. A K 3x+1 T 4x+2 5x 5x = 4x+2 -4x x = 2 KA= 4x+2 4(2)+2 8+2 10 AT= 5x 5(2) 10 TK= 3x+1 3(2)+1 6+1 7

7. Sample Problems : Triangle ABC is an equiangular with <ABC= 4x, <BCA= 3x+15, and <CAB= x+45. Find the measure of each angle. 4x x+45 3x+15 B A C 4x = 3x+15 -3x x = 15 <ABC= 4x 4(15) 60 <BCA= 3x+15 3(15)+15 45+15 60 <CAB= x+45 15+45 60 *Short cut: if a triangle is equiangular, then all angles are 60 degrees

8. Classify Triangle 1. 2. 3. 4. 5. 6. Classify each triangle by the number of congruent sides or congruent segments.Answers are on the next slide.

9. Classify Triangle 1.Equilateral 2.Right 3.Isosceles 4.Scalene 5.Obtuse 6.Equiangular Classify each triangle by the number of congruent sides or congruent segments.

10. Practice Problems: Find the measure of the sides of triangle MON and classify by its side lengths. M(-2,2), O(1,0), N(-3,-4) Go to the next side to see the answer and the work.

11. Practice Problems: Find the measure of the sides of triangle MON and classify by its side lengths. M(-2,2), O(1,0), N(-3,-4) MO= √(-2-1) 2 +(2-0) 2 √-3 2 +2 2 √9+4 √13 ON=√(1- -3) 2 +(0- -4) 2 √(1+3) 2 +(0+4) 2 √4 2 +4 2 √16+16 √32 √16·2 √16√2 4√2 NM=√(-3- -2) 2 +(-4-2) 2 √(-3+2) 2 +(-4-2) 2 √-1 2 -6 2 √1+36 √37 Since none of the sides of the triangle are the congruent, or the same length, we know that the triangle should be classified as an isosceles triangle. Distance Formula: √(x 1 -x 2 ) 2 +(y 1 -y 2 ) 2 This is used to calculate the length of each side.

12. Practice Problems: Triangle MET is an equilateral triangle,ME=3x-12, ET=4y+100, MT=5x+4y. Find the value of x and y, and the measure of side MT. Go to the next side to see the answer and the work.

13. Practice Problems: Triangle MET is an equilateral triangle,ME=3x-12, ET=4y+100, MT=5x+4y 3x-12=4y+100 +12 3x=4y+112 -4y 3x-4y=112 (Equation #1) 5x+4y=3x-12 -3x 2x+4y=12 (Equation #2) 2x+4y=-12 3x-4y=112 (Cancel out y) 5x=100 ÷5 X=20 MT=5x+4y MT=5(20)+4(-13) (Plug in x and y values) MT=100-52 MT=48 2x+4y=-12 2(20)+4y=-12 (Plug in the answer for x) 40+4y=-12 -40 4y=-52 ÷4 y=-13

14. Practice Problems: Triangle LMN is an isosceles triangle with base LN. <LMN = 12x and <MLN = x+20. Find the measures of all of the angles. Go to the next side to see the answer and the work.

15. Practice Problems: Triangle LMN is an isosceles triangle with base LN. <LMN = 12x and <MLN = x+20. Find the measures of all of the angles. 12x+2(x+20) = 180 12x+2x+40 = 180 14x+40 =180 -40 14x = 140 x = 10 <LMN = 12x 12(10) 120 <MLN = x+20 10+20 30 <MNL = 30 *If a triangle is isosceles, then the base angles are congruent.

16. Work Cited Mr. Pricci’s math packet (Honors Geometry Congruent Triangles)