Lesson 4-1
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Transcript of Lesson 4-1
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Lesson 4-1
Classifying Triangles
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5-Minute Check on Chapter 35-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 m3.
3. Find m4.
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 of¾ 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 CB D–3/2 –2/3 2/3 3/2
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5-Minute Check on Chapter 35-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 m3. 62
3. Find m4. 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 of¾ 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 CB D–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 triangle Equilateral triangle
All angles < 90 One angle > 90 One angle = 90
No sides are Two sides are All sides are
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Classifying TrianglesClassify 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 sidescongruent
2 sidescongruent
3 sidescongruent
Right
Obtuse
Acute
Scalene
Isosceles
EquilateralEquiangular3 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