Types of Angles
–Vertical Angles have equal measure. In the example below, angles 1 and 3 are vertical angles, as well as angles 2 and 4.
–Alternate Interior Angles have the same measure. As we can see expressed below, angles 1 and 2 are alternate interior angles.
–Alternate Exterior Angles have the same measure. They are on opposing sides of the transversals.
–Same Side Interior Angles – When angles are on the same side of a transversal (a line that passes through two lines in the same plane at two distinct points), they add up to 180 degrees.
–Corresponding Angles have the same measure.
The angles that are corresponding are angles 1 and 5, 2 and 6, 3 and 7, and 4 and 8. I have color-coded them to make it easier to see.
Types of Triangles
Acute Triangle
All of the angles are acute, and all the angle measure sum 180 degrees.
Right Triangle
Right triangles have one right angle and two acute angles, as seen below.
Obtuse Triangle
Obtuse triangles have one obtuse angle and two acute.
Equilateral Triangle
Equilateral triangles have all sides of equal length. When referring to equal side lengths of triangles, they are denoted by the dashes seen in the middle of the sides.
Isosceles Triangle
Isosceles triangles have two sides of equal measure.
Scalene Triangle
Scalene triangles have no sides of the same measure.
Conditions for Similar Triangles:
- Corresponding angles are equal
- Corresponding sides are proportional
Similar triangles have the same shape, but not necessarily the same size.
Congruent Triangles
Congruent triangles have the same shape and the same size (they must be similar).
Practical Application
subtract 7x from both sides
(4x+52)\degree=(7x+10)\degree \\ -7x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -7x \\-3x+52\degree=10\degree
Subtract 52 from both sides.
-3x+52\degree= 10\degree \\ -52 \ \ \ \ \ -52\\-3x\degree=-42\degree
Divide both sides by -3.
\frac{-3x\degree}{-3}=\frac{-42\degree}{-3}