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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. Vocabulary. perpendicular lines parallel lines
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Geometry Presentation #2Line and Angle Relationships & Classifying PolygonsApril 23, 2013Math Block 4 Learning Objectives: Identify parallel, perpendicular, and skew lines, and angles formed by a transversal Identify and name polygons
Vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal
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.
Reading Math The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Additional Example 1: Identifying Parallel, Perpendicular, and Skew Lines XY and WZ UV and YV XU and WZ XU and WZ are skew. XY || WZ UV YV Tell whether the lines appear parallel, perpendicular, or skew. The lines appear to intersect to form right angles. The lines are in different planes and do not intersect. The lines are in the same plane and do not intersect.
WX and XU WX XU Check It Out: Example 1A Tell whether the lines appear parallel, perpendicular, or skew. The lines appear to intersect to form right angles.
WX and UV WX and UV are skew. Check It Out: Example 1B Tell whether the lines appear parallel, perpendicular, or skew. The lines are in different planes and do not intersect.
WX and ZY WX || ZY Check It Out: Example 1C Tell whether the lines appear parallel, perpendicular, or skew. The lines are in the same plane and do not intersect.
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. 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
Reading Math Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.
A transversalis a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.
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, m2 = 130°.
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. m3 + 130° = 180° –130° –130° Subtract 130° to isolate m3. m3 = 50°
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. 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°
Side Vertex Remember! Vertices is plural for vertex. Triangles and rectangles are examples of polygons. A polygonis a closed plane figure formed by three or more line segments. Each line segment forms a sideof 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 at left has six sides and six vertices.
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.
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.
Polygons are classified by the number of sides and angles they have. Quadrilateral 4 sides 4 angles Pentagon 5 sides 5 angles Triangle 3 sides 3 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
Additional Example 2: Classifying Polygons Name each polygon. A. B. Octagon Quadrilateral
Check It Out: Example 2 Name each polygon. B. A. 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 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.
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.
