1. Prepared by: David Crockett Math Department

2. Angles If two lines cross, we say they intersect and the point where they cross is called the point of intersection. Next Two lines which are in the same plane must either intersect or not intersect. When two lines in the same plane do not intersect they are called parallel lines. Intersecting lines Parallel lines

3. Next Angles (Continued) If two lines make square corners at the point of intersection, they are called perpendicular lines and the angles formed are called right angles. We can draw a little square at the point of intersection to indicate that all four angles formed are right angles. 4 right angles

4. Next Angles (Continued) Two right angles form a straight angle. Straight angle An angle smaller than a right angle is called an acute angle. acute An angle greater than a right angle is called an obtuse angle. obtuse 2 acute angles and 2 obtuse angles

5. Next Angles (Continued) A right angle has a measure of 90 degrees. A straight angle has a measure of 180 degrees. 90° in a right angle 180° in a straight angle A circle has a measure of 360 degrees. 90° 360° in a circle

6. Polygons A polygon is a special type of geometric figure. The word polygon is formed from the Greek roots poly, which means “more than one” or “many,” and gonon, which means “angle.” Therefore, the word polygon literally means “more than one angle.” The modern understanding of a polygon is a simple, closed, flat geometric figure whose sides are line segments. The following are examples of figures that are not polygons. Next a) not a polygonb) not a polygonc) not a polygond) not a polygon lines cross not simple lines cross not simple not a closed figure has a curved side

7. Polygons (continued) Triangle 3 sides 3 vertices Quadrilateral 4 sides 4 vertices Pentagon 5 sides 5 vertices Hexagon 6 sides 6 vertices Heptagon 7 sides 7 vertices Octagon 8 sides 8 vertices Next

8. Polygons (continued) Next Each segment of a polygon is called a side. Each endpoint of a side and also the points where two sides meet is called a vertex. The plural of vertex is vertices. For each polygon, the number of sides is always equal to the number of vertices. Polygons are named according to the number of sides they have: The polygon with the fewest number of sides (3) is the triangle. A polygon with 4 sides is called a quadrilateral. A polygon with 5 sides is called a pentagon. A polygon with 6 sides is called a hexagon. A polygon with 7 sides is called a heptagon. A polygon with 8 sides is called a octagon. A polygon with 9 sides is called a nonagon. A polygon with 10 sides is called a decagon. A polygon with 11 sides is called a undecagon. A polygon with 12 sides is called a dodecagon.

9. Next Concave and Convex Polygons If a polygon has an indentation (or cave), the polygon is called a concave polygon. Any polygon that does not have an indentation is called a convex polygon. Any two points in the interior of a convex polygon can be connected by a line segment that does not cut or cross a side of the polygon. Concave polygon Convex polygon

10. Lesson 2.B Page 5 Next Regular Polygons If all the sides of a polygon have the same length, the polygon is called an equilateral polygon. Equilateral polygonEquiangular polygon If all the angles of a polygon have the same measure, the polygon is called an equiangular polygon. Polygons in which all sides are the same length and all angles have the same measure are called regular polygons. Regular polygon

11. Next Regular Polygons The following are examples of regular polygons. Regular Triangle (Equilateral Triangle) Regular Pentagon Regular Hexagon Regular Quadrilateral (Square) 60°

12. Next Triangles Remember that the polygon with the fewest number of sides is the triangle. A triangle has three sides and three angles. Equiangular Triangle Right Triangle 60° The sum of the measures of the three angles in any triangle is 180°. If the triangle has a right angle (90°), the triangle is a right triangle. Acute Triangle If all angles have a measure less than 90°, the triangle is an acute triangle. If one angle has a measure greater than 90°, the triangle is an obtuse triangle. Obtuse Triangle If all three angles have the same measure, the triangle is an equiangular triangle.

13. Next Triangles Triangles are also classifed according to the relative lengths of their sides. Isoceles Triangle An isosceles triangle is a triangle that has at least two sides of equal length. An equilateral triangle is a triangle in which the lengths of all sides are equal. Equilateral Triangle If all the sides of a triangle have different lengths, the triangle is called a scalene triangle. Scalene Triangle The lengths of the sides of a triangle and the measures of the angles opposite these sides are related. In any triangle, the angles opposite sides of equal lengths have equal measures. Also, the sides opposite angles of equal measures have equal lengths.

14. Next Quadrilaterals Trapezoid A trapezoid is a quadrilateral that has exactly two parallel sides (1 pair). A parallelogram is a quadrilateral that has at two pairs parallel sides (2 pair). A rectangle is a parallelogram with four right angles. Remember that the polygon with four (4) sides is the quadrilateral. We will discuss five different types of quadrilaterals. A rhombus is an equilateral parallelogram. Parallelogram Rectangle Rhombus Square A square is an rhombus with four right angles.

15. Next Find x. 30° 130° x°x° Remember the sum of the measures of the three angles in any triangle is 180°. Therefore, 20°

16. Next Find x and y. Remember the sides opposite angles of equal measure are equal. Therefore, 50° y°y° x°x° and 50° 80°

17. Next Find x and y. Remember the sides opposite angles of equal measure are equal. Therefore, and 110° y°y° x°x° 8 8 35°

18. Prepared by: David Crockett Math Department