Podcast
Questions and Answers
What is the sum of the interior angles of a triangle?
What is the sum of the interior angles of a triangle?
Which type of triangle has one angle measuring 90°?
Which type of triangle has one angle measuring 90°?
What is the term for a line that joins a vertex of a triangle to the midpoint of the opposite side?
What is the term for a line that joins a vertex of a triangle to the midpoint of the opposite side?
Which type of triangle has all sides of equal length?
Which type of triangle has all sides of equal length?
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What is the point where the three medians of a triangle intersect?
What is the point where the three medians of a triangle intersect?
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What is the formula used to find the values of the sides of a right triangle?
What is the formula used to find the values of the sides of a right triangle?
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What is the longest side of a right triangle called?
What is the longest side of a right triangle called?
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What is the term for a ray that forms two congruent angles?
What is the term for a ray that forms two congruent angles?
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What is the name of the segment that divides an angle into two congruent parts?
What is the name of the segment that divides an angle into two congruent parts?
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In an isosceles triangle, what is the term for the two angles that contain the base?
In an isosceles triangle, what is the term for the two angles that contain the base?
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What is the name of the triangle with at least two sides of equal length?
What is the name of the triangle with at least two sides of equal length?
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What is the name of the side of a right triangle opposite the right angle?
What is the name of the side of a right triangle opposite the right angle?
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What is the term for a segment from a vertex perpendicular to the line containing the opposite side?
What is the term for a segment from a vertex perpendicular to the line containing the opposite side?
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In a triangle, what is the relationship between the longest side and the largest angle?
In a triangle, what is the relationship between the longest side and the largest angle?
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What is the sum of the measures of the two remote interior angles of an exterior angle?
What is the sum of the measures of the two remote interior angles of an exterior angle?
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What is the condition required for the lengths of sides of a triangle?
What is the condition required for the lengths of sides of a triangle?
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What type of angles are formed by an exterior angle and its adjacent interior angle?
What type of angles are formed by an exterior angle and its adjacent interior angle?
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What is the relationship between the shortest side and the smallest angle of a triangle?
What is the relationship between the shortest side and the smallest angle of a triangle?
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Study Notes
Triangle Basics
- A triangle is a geometrical shape with 3 sides, 3 interior angles, and 3 exterior angles.
- The sum of interior angles of a triangle is always 180°.
Types of Triangles by Angle
- Right triangle: one angle measures 90°.
- Obtuse triangle: one angle measures past 90°.
- Acute triangle: all angles measure below 90°.
Types of Triangles by Sides
- Equilateral triangle: all sides are equal.
- Scalene triangle: no sides are equal.
- Isosceles triangle: 2 sides are equal.
Parts of a Triangle
- Median: a segment joining a vertex to the midpoint of the opposite side.
- Altitude: a median that is perpendicular to the line on the opposite side.
- Bisector (angle): a ray from the vertex of the triangle, forming 2 congruent angles.
- Bisector (perpendicular): a line perpendicular to 1 side, bisecting said side.
- Point of concurrency: a common point of 3 lines in a triangle.
Centers of a Triangle
- Median: type of line that is a median.
- Centroid: type of line that is an altitude.
- Orthocenter: type of line that is an angle bisector.
- Incenter: type of line that is a perpendicular bisector.
- Circumcenter: type of line that is a center.
Pythagorean Theorem
- Used to find the values for the side of a right triangle.
- The longest side of a right triangle is called the hypotenuse.
- The other sides are called legs.
- To solve, write a²+b²=c².
Basic Parts of a Triangle
- A triangle has 3 sides, 3 vertices, and 3 angles.
- Sides can be named using letters or segment notation.
- Angles can be named using capital letters or angle notation.
- Vertices can be named using capital letters.
Secondary Parts of a Triangle
- Altitude: a segment from a vertex perpendicular to the line containing the opposite side.
- Median: a segment from a vertex to the midpoint of the opposite side.
- Angle Bisector: a segment that divides an angle into two congruent parts.
Angle Relationships
- The sum of the interior angles of a triangle is always 180°.
- Exterior Angle: an angle that forms a linear pair with an interior angle.
- Remote Interior Angles: the two interior angles that are not adjacent to a given exterior angle.
- An exterior angle is equal to the sum of the two remote interior angles.
Exterior Angles
- An exterior angle and its adjacent interior angle form a linear pair.
- Exterior angles are also vertical angles.
- The measure of an exterior angle is equal to the sum of the measures of its two remote interior angles.
Triangle Inequality Theorem
- The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
Longest Side and Largest Angle
- The longest side is opposite the largest angle.
- The shortest side is opposite the smallest angle.
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Description
Learn the fundamentals of triangles, including their definition, interior and exterior angles, and types classified by angle and side. Test your understanding of right, obtuse, acute, and equilateral triangles.
