Vocab List Unit 4
by Aaron Klussmann
1. Triangle Angle Sum Theorem
1.1. The sum of the measures of the interior angles of a triangle is 180 ° .
2. Exterior Angle Theorem
2.1. the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
3. Obtuse triangle
3.1. one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180°, no triangle can have more than one obtuse angle.
4. Scalene triangle
4.1. a triangle that has three unequal sides.
5. Isosceles triangle
5.1. a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
6. Base Angles
6.1. either of the angles of a triangle that have one side in common with the base
7. Base Angles Theorem
7.1. in an isosceles triangle, the angles opposite the congruent sides are congruent.
7.2. I connected this with Base Angles because they're a big deal in the Base Angle Theorem, obviously.
8. Triangle Inequality Theorem
8.1. the sum of any 2 sides of a triangle must be greater than the measure of the third side.
9. Longest Side/Largest Angle & Shortest Side/Smallest Angle
9.1. The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle.
10. Altitude of a triangle
10.1. a line segment through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude.
11. Midsegment of a triangle
11.1. a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.
12. Right triangle
12.1. A triangle with a right angle (90*)
13. Triangle
13.1. a plane figure with three straight sides and three angles.
14. Acute triangle
14.1. with all three angles acute (less than 90°)
15. Equiangular triangle
15.1. An equiangular triangle is a triangle where all three interior angles are equal in measure. Because the interior angles of any triangle always add up to 180°, each angle is always a third of that, or 60°
16. Vertex Angle
16.1. The point about which an angle is measured is called the angle's vertex, and the angle associated with a given vertex is called the vertex angle.
17. Equilateral triangle
17.1. s a triangle in which all three sides are equal.
17.2. I connected this one with Equiangular Triangle because it needs to be equilateral to be equiangular.
18. Special Segments of a triangle
18.1. Every altitude is the perpendicular segment from a vertex to its opposite side (or the extension of the opposite side). Some altitudes overlap with a side of the triangle or meet an extended base outside the triangle. Every triangle also has three medians. Another important line in a triangle is an angle bisector.
18.2. This one was hard for me to remember so I looked up this video: https://www.youtube.com/watch?v=xEYAgTu9C8I
18.3. I connected this with Median of a Triangle and Altitude of a Triangle because they go they are part of the special segments of a triangle.
19. Angle Bisector of a triangle
19.1. a line segment that bisects one of the vertex angles of a triangle.
20. Perpendicular Bisector of a triangle
20.1. a line segment that is both perpendicular to a side of a triangle and passes through its midpoint.
20.2. I kept forgetting this one, so iI looked up this lesson: http://jwilson.coe.uga.edu/EMAT6680Fa07/O'Kelley/Assignment%204/Perpendicular%20Bisectors%20of%20a%20Triangle.html
21. Median of a triangle
21.1. a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.
22. Point of Concurrency
22.1. A point of concurrency is a place where three or more, but at least three lines, rays, segments or planes intersect in one spot.
