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HONORS GEOMETRY4.1. Classifying Triangles
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Do Now: No need to write things- just discuss with someone near you.
•What is a triangle?•How many sides does a triangle have?
•How many angles does a triangle have?
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Triangles
• For the next unit we will be talking about TRIANGLES
• And to classify triangles we can talk about either their ANGLES or their SIDES
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Realize:
•When classifying triangles by angles…. • Two angles in a triangle are always acute--- therefore, we use the third one to classify the triangles by angles!
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Types of Triangles (angles)
•1. Acute Triangle•2. Equiangular Triangle•3. Obtuse Triangle•4. Right Triangle
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Acute Triangle
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Acute Triangle
•Has 3 acute angles
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Equiangular Triangle
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Equiangular Triangle
•Has three congruent angles!
• Pause…. What are the angles equal to???
• Which means what other type of triangle do we have?
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Obtuse Triangle
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Obtuse Triangle
•One Obtuse Angle
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Right Triangle
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Right Triangle
•One Right Angle
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Example One:
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Example Two:
Classify the following triangles as acute, equiangular, obtuse, or right. Explain your reasoning.△PQR QSR△ PQS△
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You Try!
•Classify XYZ as acute, equiangular, △obtuse, or right. Explain your reasoning.
•What about XWY? WYZ? △ △
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Classifying Triangles by Sides
•1. Equilateral Triangle•2. Isosceles Triangle•3. Scalene Triangle
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Equilateral Triangle
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Equilateral Triangle
•Three Congruent Sides
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Isosceles Triangle
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Isosceles Triangle
• Two congruent sides
• PAUSE: This means what else can we call an equilateral triangle?
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Scalene Triangle
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Scalene Triangle
•No congruent sides
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Example Three:
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Example Four:
If point M is the midpoint of JL, classify JKM as equilateral, isosceles, or △
scalene. What about ? Explain your reasoning.
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You Try!
If point Y is the midpoint of VX and WY = 3.0 units, classify VWY, △and as equilateral, isosceles, or scalene. Explain your reasoning.
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Realize…. • You can double classify triangles– once by sides, once by
angles
• Example: is a __________ triangle
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Example Five: Find the measures of the sides of isosceles triangle ABC△
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You Try! • Find the measures of the sides of What type of triangle is
it?
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Triangle Angle Sum Theorem • The sum of the measures of the angles in a triangle is 180
degrees.
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How do we know!?!?!?• Let’s Prove it!
• Given: • Prove:
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Example Six: • Find x, y, and z
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Example Seven: • Find each of the number angles
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You Try! Find the measure of each numbered angle.
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Practice Problems
• Try some on your own/in small groups!• As always if you are confused/have questions don’t hesitate to call me over!
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Exit Ticket: • Find x and then classify the triangle based on the angles.