12 Chapter Congruence, and Similarity with Constructions

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Presentation transcript:

12 Chapter Congruence, and Similarity with Constructions Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

12-3 Additional Constructions Constructing a Parallel Line Constructing Angle Bisectors Constructing Perpendicular Lines Properties of Angle Bisectors The Incenter of a Triangle Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Constructing Parallel Lines Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Constructing Parallel Lines Corresponding angle method Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Constructing Angle Bisectors Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Constructing Perpendicular Lines Constructing a perpendicular to a line from a point not on the line Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Constructing Perpendicular Lines Bisecting a line segment Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 12-10a Given triangle ABC, construct an altitude from vertex A. An altitude is the segment perpendicular from a vertex to the line containing the opposite side of a triangle, so construct a perpendicular from point A to the line containing BC. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 12-10b Given triangle ABC, construct an altitude from vertex A. Notice that the altitude AD does not intersect the interior of triangle ABC. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 12-10c Given triangle ABC, construct an altitude from vertex A. Triangle ABC is a right triangle. The altitude from vertex A is the side AB. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Properties of Angle Bisectors Any point P on an angle bisector is equidistant from the sides of the angle. Any point that is equidistant from the sides of an angle is on the angle bisector of the angle. These distances are the same. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

The Incenter of a Triangle The angle bisectors of a triangle are concurrent (they intersect in a single point, the incenter) and the three distances from the point of intersection to the sides are equal. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.