Geometry Basics Flashcards
The sum of the interior angles of a polygon depends only on the number of sides in the polygon- how is this represented algebraically?
(n-2) x 180 = Sum of Interior Angles of Polygon
–> When n = # of sides
Examples:
- Triangle = 3 sides, angles sum to 180
- Quadrilateral = 4 sides, angles sum to 360
- Pentagon = 5 sides, angles sum to 540
- Hexagon = 6 sides, angles sum to 720
The angles in ANY given triangle abide by 2 key properties, what are they?
1) The sum of the interior angles is 180
2) Angles correspond to their opposite sides
- Largest angle is opposite largest side
- Smallest angle is opposite smallest side
- If two sides are equal, their opposite angles are also equal
What is the Triangle Inequality Law?
The sum of any two sides of a triangle must be GREATER THAN the third side (cannot equal the third side).
Likewise…the length of the third side must also be GREATER THAN the difference between the any two sides
**If you are given 2 sides of a triangle, the length of the third side must fall between the difference and sum of the two given sides.
What is one reason an Isosceles Right Triangle is so important?
Two Isosceles Right Triangles (when combined) form a perfect square!
Therefore when given the diagonal of a square, you can use the 45-45-90 ratio to find the length of a side of the square.
What are considered Similar Triangles?
Triangles are said to be “Similar” if their corresponding angles are equal and their corresponding sides are in proportion.
**If you find that 2 angles of a triangle are the equal, then the third angles must be equal as a result of the properties of triangles. Thus, the triangles are similar
What is the relationship betweeen side length and triangle area for similar triangles?
If two similar triangles have corresponding side lengths in the ration of a:b, then their areas will be in ratio a2:b2
What are the relationships between the Radius, Diameter, Circumference, and Area of a circle?
How do you find a specified arc length of a circle?
The arc’s length is in proportion to its central angle. Thus if the central angle of the arc is 60 degrees, then the arc length will be 1/6 of the circumference (since 60 is 1/6 of 360)
How do you find the area of a sector
Similar to finding the length of an arc, the area of a sector will depend upon its central angle. If the central angle of a sector is 60 degrees, then the area of the sector will be 1/6 of the area of the circle (since 60 is 1/6 of 360).
How do you find the perimeter of a sector?
A sector is composed of 2 radii and 1 arc. Thus, the perimeter is equal to the sum of the length of the 2 radii and the length of the arc.
What is the definition of a central angle?
A central angle is an angle whose vertex lies at the center point of a circle.
What is the definition of an inscribed angle? What is the relation of an inscribed angle to the respective arc it intercepts?
An inscribed angle is one that has its vertex on the cirlce iteslef (angle falls on the circumference line).
An inscribed angle is exactly 1/2 of the arc it intercepts (in degrees)
What is an Inscribed Triangle and what is the rule for if one side of an inscribed triangle is a diameter of the circle?
What do the interior angles formed by intersecting lines sum to?
Interior angles formed by intersecting lines form a cirlce, so the sume of these angles is 360 degrees
What are supplementary angles?
Supplementary angles are interior angles that combine to form a line (thereby sum 180 degrees)
What are Vertical Angles?
Vertical Angles are equal angles found opposite each other where the lines intersect. They are equal!!!!
What is the Exterior Angle of a triangle? What is the Exterior Angle equal to?
What is an acute angle?
An acute angle is an angle less than 90 degrees
What is an obtuse angle?
An obtuse angle is an angle more than 90 degrees but less than 180 degrees
Acute angles are supplementary to obtuse angles
What are the properties of angles formed by parallel lines cut by a transversal?
- With two parallel lines and a transveral, there are a total of 8 angles that are formed- however there are only 2 different angle measures.
- All the acute angles are equal to each other.
- All the obtuse angles are equal to one another
- The acute and obtuse angles are supplementary (sum to 180)
What are the 4 types of Slope?
vertical line = undefined slope = y axis
horizontal line = no slope = x axis
Where are Quadrants 1 through 4 on a coordinate plane?
