1. Geometry Presentation #2 Line and Angle Relationships & Classifying Polygons April 23, 2013 Math Block 4
Learning Objectives:
Identify parallel, perpendicular, and skew lines, and angles formed by a transversal
Identify and name polygons

2. Vocabulary perpendicular lines parallel lines skew lines
adjacent angles
vertical angles
transversal

3. When lines, segments, or rays intersect, they form angles
When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines measure 90°, the lines are perpendicular lines.
Some lines in the same plane do not intersect at all. These lines are parallel lines. Segments and rays that are part of parallel lines are also parallel.
Skew lines do not intersect, and yet they are also not parallel. They lie in different planes.

4. The symbol means “is parallel to
The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Reading Math

5. Additional Example 1: Identifying Parallel, Perpendicular, and Skew Lines
Tell whether the lines appear parallel, perpendicular, or skew.
UV and YV
The lines appear to intersect to form right angles.
UV  YV
XU and WZ
The lines are in different planes and do not intersect.
XU and WZ
are skew.
XY and WZ
The lines are in the same plane and do not intersect.
XY || WZ

6. Check It Out: Example 1A
Tell whether the lines appear parallel, perpendicular, or skew.
WX and XU
WX  XU
The lines appear to intersect to form right angles.

7. Check It Out: Example 1B
Tell whether the lines appear parallel, perpendicular, or skew.
WX and UV
The lines are in different planes and do not intersect.
WX and UV
are skew.

8. Check It Out: Example 1C
Tell whether the lines appear parallel, perpendicular, or skew.
WX and ZY
The lines are in the same plane and do not intersect.
WX || ZY

9. Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary
Vertical angles are the opposite angles formed by two intersecting lines. Angles 1 and 3 in the diagram are vertical angles. Vertical angles have the same measure, so they are congruent.

10. Reading Math
Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

11. A transversal is a line that intersects two or more lines
A transversal is a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.

13. Additional Example 2A: Using Angle Relationships to Find Angle Measures
Line n line p. Find the measure of the angle. 2
2 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.

14. Line n line p. Find the measure of the angle.
Additional Example 2B: Using Angle Relationships to Find Angle Measures
Line n line p. Find the measure of the angle. 3
Adjacent angles formed by two intersecting lines are supplementary.
m ° = 180°
–130°
–130°
Subtract 130° to isolate m3.
m3 = 50°

15. Additional Example 2C: Using Angle Relationships to Find Angle Measures
Line n line p. Find the measure of the angle. 4
Alternate interior angles are congruent. m4 = 130°.

16. Lesson Homework – Bring Answers to next class
Tell whether the lines appear
parallel, perpendicular, or skew.
1. AB and CD
2. EF and FH
3. AB and CG
4. In the figure on the right, line x || line y. Identify the measures of 2, 6, and 7.
A. 70°, 110°, 70°
B. 110°, 70°, 70°
C. 70°, 70°, 110° 16

17. segment at a common point. This common point is a vertex of a polygon.
Triangles and rectangles are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. Each line segment forms a side of the polygon, and meets, but does not cross, another line
segment at a common point. This common point is a vertex of a polygon.
Side
Vertex
The polygon at
left has six
sides and six
vertices.
Vertices is plural for vertex.
Remember!

18. Additional Example 1: Identifying Polygons
Determine whether each figure is a polygon. If it is not, explain why not. A. B.
The figure is a polygon. It is a closed figure with 4 line segments.
The figure is not a polygon. It is not a closed figure.

19. Additional Example 1: Identifying Polygons
Determine whether each figure is a polygon. If it is not, explain why not. C. D.
The figure is not a polygon. The figure is not formed by line segments.
The figure is not a polygon. There are line segments in the figure that intersect.

20. Polygons are classified by the number of sides and angles they have.
Triangle
3 sides
3 angles
Quadrilateral
4 sides
4 angles
Pentagon
5 sides
5 angles
Hexagon
6 sides
6 angles
Heptagon
7 sides
7 angles
Octagon
8 sides
8 angles
Nonagon
9 sides
9 angles
Decagon
10 sides
10 angles

21. Additional Example 2: Classifying Polygons
Name each polygon. A. B.
Octagon
Quadrilateral

22. Check It Out: Example 2
Name each polygon. B. A.
Quadrilateral
Pentagon

23. A regular polygon is a polygon in which all sides are congruent and all angles are congruent.

24. Additional Example 3: Identifying and Classifying Regular Polygons
Name each polygon and tell whether it is a
regular polygon. If it is not, explain why not. B. A.
The figure is a
quadrilateral. It is an
irregular polygon because all of the sides are not congruent.
The figure is a regular
quadrilateral. A regular quadrilateral is also called a square.

25. Lesson Homework – Bring Answers to next class
Determine whether each figure is a polygon. If it in not, explain why not. Name each polygon. 1. 2. 3. 4.
5. Tell whether each figure above is a regular polygon. If it is not, explain why not. 25