Questions and Answers
What does the Triangle Interior Angle Sum Theorem state?
All three interior angles in a triangle sum to 180 degrees.
What does the Triangle Inequality Theorem state?
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
What is a scalene triangle?
What defines an isosceles triangle?
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What is an equilateral triangle?
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What are vertical angles?
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What is a linear pair?
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What is a right triangle?
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What is an obtuse triangle?
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What is an acute triangle?
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What is the hypotenuse of a right triangle?
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What does the Sides and Angles Inequality in a Triangle Theorem state?
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What is a leg of a right triangle?
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What is the Converse of the Pythagorean Theorem?
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What is the Pythagorean Theorem?
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What does the Triangle Exterior Angle Theorem state?
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Study Notes
Key Theorems and Definitions
- Triangle Interior Angle Sum Theorem: The sum of all three interior angles in any triangle is always 180 degrees.
- Triangle Inequality Theorem: For any triangle, the sum of the lengths of two sides must always be greater than the length of the third side.
- Sides and Angles Inequality in a Triangle Theorem: In a triangle, a longer side correlates with a larger opposite angle.
Types of Triangles
- Scalene Triangle: Defined by having no congruent sides, meaning all sides are of different lengths.
- Isosceles Triangle: Features at least two congruent sides, allowing for two equal angles as well.
- Equilateral Triangle: A special type of isosceles triangle where all three sides and angles are congruent (60 degrees each).
- Right Triangle: Contains one right angle (90 degrees) among its three angles.
- Obtuse Triangle: Has one angle that measures greater than 90 degrees.
- Acute Triangle: All three angles in this triangle measure less than 90 degrees.
Important Angle Concepts
- Vertical Angles: Formed by two intersecting lines creating a pair of opposite, congruent angles.
- Linear Pair: A pair of adjacent angles formed when two lines intersect, with their noncommon sides being opposite rays.
Triangle Specifics
- Hypotenuse: In a right triangle, this is the side opposite the right angle, and it is the longest side.
- Legs of a Right Triangle: The two sides that form the right angle in a right triangle.
Theorems Related to Right Triangles
- Pythagorean Theorem: Relates the lengths of the legs and hypotenuse in a right triangle with the formula a² + b² = c².
- Converse of the Pythagorean Theorem: Indicates that if the squares of two sides of a triangle equal the square of the third side, the triangle is right-angled.
Angle Relationships
- Triangle Exterior Angle Theorem: Each exterior angle of a triangle is equal to the sum of the two remote interior angles.
Studying That Suits You
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Description
Test your knowledge on the properties of triangles with these flashcards. This quiz covers important theorems such as the Triangle Interior Angle Sum Theorem and the Triangle Inequality Theorem, as well as different types of triangles. Perfect for students wanting to reinforce their understanding of triangle properties.
