Download Shapes and Designs Notes Complementary Angles: Angles that add

Shapes and Designs Notes
Complementary Angles: Angles that add up to 90 degrees
Supplementary Angles: Angles that add up to be 180 degrees
Polygon: A closed shape formed of 3 or more straight line segments. A regular polygon is a polygon in
which all sides are equal and all angles are equal.
Sum of angles in a polygon: ( n − 2 ) ⋅180! where n is the number of sides
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To find a single interior angle in a regular polygon:
1. Find the total sum of all interior angles (see above)
2. Divide the sum of the interior angles by the number of sides.
Sum of exterior angles in a polygon: 360 degrees for all
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To find a single exterior angle in a regular polygon, divide 360 by the number of sides
Triangle inequality: Given 3 lengths a, b, and c, where c is the longest, a triangle will only be made if
a+b >c
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It helps to list the sides from least to greatest
If a + b < c you get an open triangle
If a + b = c you get a straight line
If a triangle can be made, only one is possible.
Triangle Uniqueness: Unique triangles are made for SSS, SAS, ASA, and AAS
Quadrilateral inequality: Given 4 lengths a,b,c,d, where d is the longest, you only get a quadrilateral if
a+b+c>d.
• It helps to list the sides in order from least to greatest if possible.
• If a quadrilateral can be made, there is not a unique quadrilateral from those lengths
• Rectangles and parallelograms can be formed if you have 2 pairs of equal lengths
• Squares and rhombuses can be made if all 4 sides are the same length
Vertical Angles: Vertical angles are angles that are opposite of each other when two lines intersect. They
are always equal
Parallel lines cut by a transversal
If a transversal line cuts two parallel lines, then the acute angles are equal and the obtuse angles are equal.
If the lines are not parallel, this does not hold true.
In the pictures above, angles 1, 4, 5, and 8 are all equal while 2, 3, 6, and 7 are also all equal.