1. 12 Chapter Congruence, and Similarity with Constructions
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2. 12-3 Additional Constructions
Constructing a Parallel Line
Constructing Angle Bisectors
Constructing Perpendicular Lines
Properties of Angle Bisectors
The Incenter of a Triangle
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3. Constructing Parallel Lines
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4. Constructing Parallel Lines
Corresponding angle method
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5. Constructing Angle Bisectors
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6. Constructing Perpendicular Lines
Constructing a perpendicular to a line from a point not on the line
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7. Constructing Perpendicular Lines
Bisecting a line segment
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8. 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.
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9. 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.
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10. 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.
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11. 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.
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12. 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.
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