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Questions and Answers
What is the definition of a scalene triangle?
What is the definition of a scalene triangle?
- 3 acute angles
- All 3 sides congruent
- No sides congruent (correct)
- At least 2 sides congruent
What is the definition of an isosceles triangle?
What is the definition of an isosceles triangle?
- No sides congruent
- All 3 sides congruent
- 1 obtuse angle
- At least 2 sides congruent (correct)
What defines an equilateral triangle?
What defines an equilateral triangle?
- All 3 sides congruent (correct)
- 1 right angle
- 3 acute angles
- At least 2 sides congruent
What is the definition of an acute triangle?
What is the definition of an acute triangle?
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What defines a right triangle?
What defines a right triangle?
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What is the definition of an obtuse triangle?
What is the definition of an obtuse triangle?
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What is the definition of an equiangular triangle?
What is the definition of an equiangular triangle?
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The distance formula is used to find _____ between two points.
The distance formula is used to find _____ between two points.
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How do you find the sides of a triangle using the distance formula and determine if it's a right angle?
How do you find the sides of a triangle using the distance formula and determine if it's a right angle?
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Study Notes
Triangle Classifications
- Scalene: A triangle with no sides that are congruent, meaning all sides have different lengths.
- Isosceles: Features at least two sides that are congruent, which results in two equal angles opposite those sides.
- Equilateral: All three sides are congruent, leading to all three angles also being congruent at 60 degrees each.
Angle Classifications
- Acute: A triangle where all three angles are acute, each measuring less than 90 degrees.
- Right: Contains one right angle that measures exactly 90 degrees, while the other two angles are acute.
- Obtuse: Includes one obtuse angle, which measures more than 90 degrees but less than 180 degrees.
Additional Terminology
- Equiangular: A triangle in which all three angles are congruent, each being 60 degrees in the case of equilateral triangles.
Distance Formula Usage
- The distance formula is essential for finding the lengths of the sides of a triangle using the coordinates of its vertices.
Right Angle Determination
- Check for right angles by using slopes (rise/run) to identify perpendicular lines; if two lines have negative reciprocal slopes, they form a right angle.
- Solve for side lengths using the distance formula and keep the results in radical form to ensure accuracy.
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