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Lesson 4-1

Lesson 4-1. Classifying Triangles. Transparency 4-1. 5-Minute Check on Chapter 3. Refer to the figure. 1. What is the special name given to the pair of angles shown by  2 and  6? 2. Find m  3. 3. Find m  4 . 4. Find the slope of the line that contains the points at (4, 4) and

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Lesson 4-1

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  1. Lesson 4-1 Classifying Triangles

  2. Transparency 4-1 5-Minute Check on Chapter 3 Refer to the figure. 1. What is the special name given to the pair of anglesshown by 2 and 6? 2. Find m3. 3. Find m4. 4. 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: A B C D 3/2 –3/2 2/3 –2/3

  3. Transparency 4-1 5-Minute Check on Chapter 3 Refer to the figure. 1. What is the special name given to the pair of anglesshown by 2 and 6? corresponding angles 2. Find m3. 62 3. Find m4. 118 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 + 5 6. What is the slope of a line that is perpendicular to the line y = 2/3x – 5? Standardized Test Practice: A B C D 3/2 –3/2 2/3 –2/3

  4. Objectives • Identify and classify triangles by angles • Identify and classify triangles by sides

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

  6. Classifying Triangles … By angles Acute triangle Obtuse triangle Right triangle All angles < 90 One angle > 90 One angle = 90 … By sides Scalene triangle Isosceles triangle Equilateral triangle No sides are  Two sides are  All sides are 

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

  8. ARCHITECTURE The triangular truss below is modeled for steel construction. Classify JMN, JKO, and OLNas 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.

  9. 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.

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

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

  12. ALGEBRA Find d and the measure of each side of equilateral triangleKLMif 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.

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

  14. ALGEBRA Find dand the measure of each side of equilateral triangle if and Answer:

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

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

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

  18. 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

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