GEOMETRY PRESENTATION #2LINE AND ANGLE RELATIONSHIPS & CLASSIFYING POLYGONSAPRIL 23, 2013MATH BLOCK 4Learning Objectives:

Identify parallel, perpendicular, and skew lines, and angles formed by a transversal

Identify and name polygons

Vocabulary

perpendicular linesparallel linesskew linesadjacent anglesvertical anglestransversal

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.

The symbol means “is parallel to.” The symbol means “is perpendicular to.”

Reading Math

Tell whether the lines appear parallel, perpendicular, or skew.

Additional Example 1: Identifying Parallel, Perpendicular, and Skew Lines

The lines appear to intersect to form right angles.

UV and YV

UV YV

XU and WZ

XU and WZ are skew.

The lines are in different planes and do not intersect.

XY and WZ

XY || WZ

The lines are in the same plane and do not intersect.

Tell whether the lines appear parallel, perpendicular, or skew.

Check It Out: Example 1A

The lines appear to intersect to form right angles.

WX and XUWX XU

Tell whether the lines appear parallel, perpendicular, or skew.

Check It Out: Example 1B

The lines are in different planes and do not intersect.

WX and UV

WX and UV are skew.

Tell whether the lines appear parallel, perpendicular, or skew.

Check It Out: Example 1C

The lines are in the same plane and do not intersect.

WX and ZY

WX || ZY

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 supplementaryVertical 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.

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

Reading Math

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

Line n line p. Find the measure of the angle.

Additional Example 2A: Using Angle Relationships to Find Angle Measures

22 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.

Line n line p. Find the measure of the angle.

Additional Example 2B: Using Angle Relationships to Find Angle Measures

3

m3 + 130° = 180°

–130° –130°

m3 = 50°

Adjacent angles formed by two intersecting lines are supplementary.

Subtract 130° to isolate m3.

Line n line p. Find the measure of the angle.

Additional Example 2C: Using Angle Relationships to Find Angle Measures

4

Alternate interior angles are congruent. m4 = 130°.

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°

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.

The polygon atleft has sixsides and sixvertices.

Vertices is plural for vertex.

Remember!

Side

Vertex

Determine whether each figure is a polygon. If it is not, explain why not.

Additional Example 1: Identifying Polygons

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.

Determine whether each figure is a polygon. If it is not, explain why not.

Additional Example 1: Identifying Polygons

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.

Polygons are classified by the number of sidesand angles they have.

Triangle3 sides

3 angles

Quadrilateral4 sides

4 angles

Pentagon5 sides

5 angles

Hexagon6 sides

6 angles

Heptagon7 sides

7 angles

Octagon8 sides

8 angles

Nonagon9 sides

9 angles

Decagon10 sides

10 angles

Name each polygon.

Additional Example 2: Classifying Polygons

A.

Octagon

B.

Quadrilateral

Check It Out: Example 2

Name each polygon.

A. B.

Quadrilateral Pentagon

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

Additional Example 3: Identifying and Classifying Regular Polygons

Name each polygon and tell whether it is aregular polygon. If it is not, explain why not.

The figure is a regularquadrilateral. A regular quadrilateral is also called a square.

The figure is aquadrilateral. It is an irregular polygon because all of the sides are not congruent.

A. B.

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.