Lesson 4-1 Classifying Triangles

5-Minute Check on Chapter 3 Transparency 4-1 Refer to the figure. 1. What is the special name given to the pair of angles shown by  2 and  6? 2. Find m  Find m  Find the slope of the line that contains the points at (4, 4) and (2, –5). 5. Write the equation of a line in slope-intercept form that has a slope of ¾ and contains the point at (0, 5). 6. What is the slope of a line that is perpendicular to the line y = 2/3x – 5? Standardized Test Practice: ACBD –3/2 –2/3 2/3 3/2

5-Minute Check on Chapter 3 Transparency 4-1 Refer to the figure. 1. What is the special name given to the pair of angles shown by  2 and  6?corresponding angles 2. Find m  3.62  3. Find m   4. Find the slope of the line that contains the points at (4, 4) and (2, –5).9/2 5. Write the equation of a line in slope-intercept form that has a slope of ¾ and contains the point at (0, 5).y = 3/4x What is the slope of a line that is perpendicular to the line y = 2/3x – 5? Standardized Test Practice: ACBD –3/2 –2/3 2/3 3/2

Objectives Identify and classify triangles by angles Identify and classify triangles by sides

Vocabulary Scalene – no sides are congruent Isosceles – two sides are congruent Equilateral – all sides are congruent Equiangular – all angles are congruent

Classifying Triangles … By angles … By sides Acute triangle Obtuse triangle Right triangle Scalene triangle Isosceles triangleEquilateral triangle All angles 90One angle = 90 No sides are  Two sides are  All sides are 

Classifying Triangles Classify by angle measure Classify by number of congruent sides Angles Sides Measure of one angle is 90° Measure of all angles < 90° Measure of one angle > 90° No sides congruent 2 sides congruent 3 sides congruent Right Obtuse Acute Scalene Isosceles Equilateral Equiangular 3 congruent angles

ARCHITECTURE The triangular truss below is modeled for steel construction. Classify  JMN,  JKO, and  OLN as acute, equiangular, obtuse, or right. Answer:  JMN has one angle with measure greater than 90 , so it is an obtuse triangle.  JKO has one angle with measure equal to 90 , so it is a right triangle.  OLN is an acute triangle with all angles congruent, so it is an equiangular triangle.

ARCHITECTURE The frame of this window design is made up of many triangles. Classify  ABC,  ACD, and  ADE as acute, equiangular, obtuse, or right. Answer:  ABC is acute.  ACD is obtuse.  ADE is right.

Answer:  UTX and  UVX are isosceles. Identify the indicated triangles in the figure if Isosceles triangles have at least two sides congruent. Isosceles triangles Scalene triangles Answer:  VYX,  ZTX,  VZU,  YTU,  VWX,  ZUX, and  YXU are scalene. Scalene triangles have no congruent sides.

Identify the indicated triangles in the figure. a. isosceles triangles b. scalene triangles Answer:  ABC,  EBC,  DEB,  DCE,  ADC,  ABD Answer:  ADE,  ABE

ALGEBRA Find d and the measure of each side of equilateral triangle KLM if KL = d + 2, LM = 12 – d and KM = 4d – 13. Since  KLM is equilateral, each side has the same length. So KL = KM. Substitution Subtract d from each side. Add 13 to each side. Divide each side by 3.

Next, substitute to find the length of each side. Answer: For  KLM, and the measure of each side is 7.

Answer: ALGEBRA Find d and the measure of each side of equilateral triangle if and

COORDINATE GEOMETRY Find the measures of the sides of  RST. Classify the triangle by sides.

Answer: ; since all 3 sides have different lengths,  RST is scalene. Use the distance formula to find the lengths of each side.

Find the measures of the sides of  ABC. Classify the triangle by sides. Answer: ; since all 3 sides have different lengths,  ABC is scalene.

Summary & Homework Summary: –Triangles can be classified by their angles as acute, obtuse or right –Triangles can be classified by their sides as scalene, isosceles or equilateral Homework: –pg 180-1: 5, 9, 13-18, 27