Download Section 4.1 ~ Triangle Sum Properties

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Transcript
Section 4.1 ~ Triangle Sum Properties
Topics in this lesson:
• classification of triangles
• Triangle Sum Theorem
• Exterior Angle Theorem
• interior & exterior angles
• corollary
Classifying Triangles by Sides
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
No ≅ sides
At least 2 ≅ sides
3 ≅ sides
Classifying Triangles by Angles
Acute Triangle
3 acute angles
Right
Triangle
1 right angle
Obtuse
Triangle
1 obtuse angle
Equiangular
Triangle
3 ≅ angles
Example 1
Draw an isosceles right triangle.
Draw an obtuse scalene triangle.
.
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Example 2
Classify RST by its sides. Then determine if the triangle is a right triangle.
Step 1: Find the lengths of the sides.
RT = RS = ST = Step 2: Check slopes for a right angle.
RT = ST = Classification: Always be as specific as you can. If you can classify by angles AND sides, do so.
Vocabulary
interior angle
interior angles ­ the original inside angles when the sides of a polygon are extended
exterior angle
exterior angles ­ the angles that form linear pairs with the interior angles when the sides of a polygon are extended
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Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180o.
180o
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Example 3
Use the diagram at the right
to find the measure of DCB.
Example 4
Find the measure of 1 in the diagram.
4.1
3
Vocabulary
corollary to a theorem ­ a statement that usually follows a theorem that can be proven easily using a theorem
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary.
90o
Example 5
The front face of the wheelchair ramp shown forms a right triangle. The measure of one acute angle in the triangle is eight times the measure of the other. Find the measure of each acute angle.
What is the measure of the obtuse angle formed between the ramp and a segment extending from the horizontal leg?
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