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Applications of the Distance Formula
Unit 4 Day 9
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Classifying Triangles by Sides
Scalene Triangle Isosceles Triangle Equilateral Triangle No congruent sides At least 2 congruent sides 3 congruent sides
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Classifying Triangles by Angles
Acute Triangle Right Triangle Obtuse Triangle Equiangular Triangle 3 acute angles 1 right angle 1 obtuse angle 3 congruent angles
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Example 1 A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. A(2,3), B(6,3), C(2,7) AB = 6− −3 2 AB = AB = 16 AB = 4 C A B
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Example 1 Continued A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. A(2,3), B(6,3), C(2,7) AC = 2− −3 2 AC = AC = 16 AC = 4 C A B
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Example 1 Continued A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. A(2,3), B(6,3), C(2,7) BC = 2− −3 2 BC = − BC = BC = 32 BC = 4 2 ≈5.66 A B C
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Example 1 Continued A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. A(2,3), B(6,3), C(2,7) AB = 4 AC = 4 BC = 4 2 ≈5.66 2 congruent sides: Isosceles Triangle 1 Right Angle: Right Triangle A B C
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Example 2 The center of a circle is C(-3, 5) and the point P(5,11) is on the circle. Find the radius of the circle. CP = 5− − −5 2 CP = CP = CP = 100 CP = 10 Radius = 10
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Example 3 A circle has its center at (-2,5) and a radius of 5. For the point below determine whether the point is on the circle, inside the circle, or outside the circle. Justify your answers. (3, -2) CP = 3− − −2−5 2 CP = CP = 74 ≈8.60 (3,-2) lies outside the circle because 8.60 >5 If the distance between the Center and the Point (CP) : CP > r P is outside CP = r P is on CP < r P is inside
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