1. Angles and Phenomena in the World
Section 10.3
Angles and Phenomena in the World

2. Reflections
Def: A normal line at a point on a surface is the line that passes through that point and is perpendicular to the surface at that point.
Law of Reflection: Incoming and reflected light rays make the same angle with the normal line at the point where the incoming light ray hits the surface.

3. Section 10.4
Circles and Spheres

4. Definition of a Circle
Def: A circle is the collection of all the points in a plane that are a fixed distance away from a certain point.
Def’s: The fixed point is the center and the distance is the radius. The diameter is the distance from a point on the circle to the point “opposite” of it.

5. Example Problem
Ex 1: Lexington and Louisville are 75 miles apart. Stephanie lives 30 miles from Lexington and 90 miles from Louisville. Is it possible to know exactly where Stephanie lives from this information?

6. Definition of a Sphere
Def: A sphere is the collection of all points in space that are a fixed distance away from a certain point.
Def’s: Center, radius, and diameter are defined as before.

7. Section 10.5
Polygons

8. Plane Shapes
Def: A plane shape or 2-dimensional shape (or shape) is a flat region that lies in the plane that is connected and closed.
If the shape is made of line segments, every endpoint of a segment must meet at exactly one endpoint of another segment, and segments are not allowed to cross.

9. 4-sided Shapes
Def: A quadrilateral is a closed shape in a plane consisting of 4 line segments that do not cross
What properties of shapes help us categorize or classify them?
Number of sides
If any sides are parallel
If any side lengths are equal
The size of the angles
Symmetry?

10. Classification of Quadrilaterals
Square- quadrilateral with 4 right angles whose sides all have the same length
Rectangle- quadrilateral with 4 right angles
Rhombus (Diamond)- quadrilateral whose sides all have the same length
Parallelogram- quadrilateral for which opposite sides are parallel
Trapezoid- quadrilateral for which at least one pair of opposite sides are parallel

11. 3-sided Shapes
Def: A triangle is a closed plane shape made of 3 line segments.
Special Triangles:
A right triangle is a triangle that has a right angle. The side opposite of the right angle is the hypotenuse.
A triangle with 3 sides of the same length is an equilateral triangle.
A triangle with at least 2 sides of the same length is an isosceles triangle.
A triangle whose angles are all smaller than 90˚ is an acute triangle, and one with an angle greater than 90˚ is an obtuse triangle.

12. Identifying Triangles
Ex: Identify whether each of the following are right, equilateral, isosceles, acute, and/or obtuse triangles.

13. Polygons
Def: A polygon is a plane shape consisting of a finite number of line segments.
𝑛-gon: polygon with 𝑛 sides and vertices
3-gon: triangle
4-gon: quadrilateral
5-gon: pentagon
6-gon: hexagon
8-gon: octagon
12-gon: dodecagon
Def: A polygon is regular if all sides have the same length and all angles are equal.
Theorem: The interior angles of the regular 𝑛-gon are
180− 360 𝑛

14. Venn Diagrams
Venn Diagrams: use ovals to show how certain sets, or collections of objects, are related