triangles geometry mr. zampetti unit 3, day 1. today’s objectives to learn new strategies that...
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Triangles
Geometry
Mr. Zampetti
Unit 3, Day 1
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Today’s Objectives
• To learn new strategies that will help find the measures of angles in a triangle
• To learn how to classify triangles
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Triangle Activity
1. Draw and cut out a large triangle.
2. Number all three angles of the triangle
3. Tear of the angles
4. Place the 3 angles adjacent to each other to form one angle
• Compare your results with a partner.• Make a conjecture about the sum
of the angles of a triangle.
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Theorem 2-1Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180.
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Video: Sum of the Angles of a Triangle
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Find the measure of the missing angle
http://www.mathsisfun.com/geometry/images/triangle-missing-angle.gifhttp://maths.fallibroome.cheshire.sch.uk/triangle.jpg
http://www.gizapyramid.com/basic_triangle_w-angles.gif
x
x
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Practice
• Find all Variables:
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Practice
• Find all Variables:
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Practice
• Find all variables
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Definition
Exterior Angle: an angle formed by the side of a polygon and an extension of a side.
http://www.freemathhelp.com/images/lessons/exterior1.gif
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Definition
Remote Interior Angle: the two nonadjacent interior angles to an exterior angle.
http://www.freemathhelp.com/images/lessons/exterior1.gif
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Activity!
• Draw a triangle with an Exterior Angle like this:
• Measure all of the angles.• With a partner, make a conjecture about
the exterior angle and the remote interior angles.
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Theorem 2-2Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
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Find the measure of the missing angle
http://www.kwiznet.com/px/homes/i/grade8/math/Grade_VIII_Triangles_And_Polygons_PB2_QuestionNo.5.gif
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Find the measure of the missing angle
http://www.freemathhelp.com/images/lessons/exterior2.gif
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Definition
Corollary: a statement that follows directly from a theorem.
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Corollary to Theorem 2-2
The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.
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Types of Triangles (by sides)
• Equilateral
• Isosceles
• Scalene
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Equilateral Triangles
• Definition:– A triangle with three
congruent sides.
• Example:
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Isosceles Triangles
• Definition:– A triangle with two
congruent sides.
• Example:
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Scalene Triangles
• Definition:– A triangle with no
congruent sides.
• Example:
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Types of Triangles (by angle)
• Equiangular
• Acute
• Right
• Obtuse
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Equiangular Triangles
• Definition:– A triangle with three
congruent angles.
• Example:
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Acute Triangles
• Definition:– A triangle whose
angles are all acute.
• Example:
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Right Triangles
• Definition:– A triangle with one
right angle.
• Example:
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Obtuse Triangles
• Definition:– A triangle with one
obtuse angle.
• Example:
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Triangle Video
• Triangle video!!
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Homework
Work Packet: Triangles