This is the "3.2: Proof and Perpendicular Lines" page of the "Geometry Chapter 3" guide.
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Geometry Chapter 3   Tags: geometry, mahlman, math  

Last Updated: Feb 19, 2014 URL: http://libguides.mpsaz.net/content.php?pid=109598 Print Guide RSS Updates

3.2: Proof and Perpendicular Lines Print Page
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Theorems

If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

 

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

Fig. 1: The line AB is perpendicular to the line CD, because the two angles it creates (indicated in orange and blue, respectively) are each 90 degrees.

If two lines are perpendicular then they intersect to form four right angles.

Two Column

Paragraph

Flow

This is the most formal type of proof. It lists numbered statements in the left column and a reason for each statement in the right column This type of proof describes the logical argument with sentences. It is more conversational than a two-column proof. This Type of proof uses the same statements and reasons as a two-column proof, but the logical flow connecting the statements is indicated by arrows.

Statement

Reasons

1.  <@ <X

    <@<Y

    BC @ YZ

1. Given

2. <@ <Z

2.Transitive

3. DABC@DXYZ

3. ASA

If <@<X; <@<Y; BC @YZ then we know that <@<Z by the transitive property of angles. By the ASA postulate we now know DABC@DXYZ.
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