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Lesson 4-1 Classifying Triangles
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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 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: ACBD –3/2 –2/3 2/3 3/2
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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 4.118 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: ACBD –3/2 –2/3 2/3 3/2
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Objectives Identify and classify triangles by angles Identify and classify triangles by sides
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Vocabulary Scalene – no sides are congruent Isosceles – two sides are congruent Equilateral – all sides are congruent Equiangular – all angles are congruent
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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
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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
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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.
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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.
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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.
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Identify the indicated triangles in the figure. a. isosceles triangles b. scalene triangles Answer: ABC, EBC, DEB, DCE, ADC, ABD Answer: ADE, ABE
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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.
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Next, substitute to find the length of each side. Answer: For KLM, and the measure of each side is 7.
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Answer: ALGEBRA Find d and the measure of each side of equilateral triangle if and
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COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides.
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Answer: ; since all 3 sides have different lengths, RST is scalene. Use the distance formula to find the lengths of each side.
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Find the measures of the sides of ABC. Classify the triangle by sides. Answer: ; since all 3 sides have different lengths, ABC is scalene.
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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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