PIL 01
Use complementary, supplementary and congruent to compare two angles.
The first two angles in the diagram are congruent (without rigorously defining congruent, you can tell because they have the same markings).
The next two angles are complementary (they add up to 90°). The last two angles are supplementary (their measures add up to 180°). |
PIL 02Given two intersecting lines, identify Linear Pairs and Vertical Angles. Use Theorems of these angle pairs to solve problems.
Linear pairs are two adjacent, supplementary angles (their non-shared sides form a line). They are usually formed when two lines intersect.
Vertical angles are angles who's sides form two intersecting lines. They also share a vertex and are always complimentary. Find the linear pairs and vertical angles at right and then solve for angle measures. |
PIL 03Prove Linear Pair Theorem.
Conditional: If two angles form a linear pair, then they are supplementary.
QED
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Image courtesy of mathwarehouse.com
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PIL 05Given a pair of lines cut by a transversal, identify Corresponding, Alternate Interior, Alternate Exterior, Same Side Interior, Same Side Exterior angles. Solve problems using these ideas.
In any pair of lines
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Image courtesy of glogster.com
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PIL 05aDefine parallel lines (translation) and perpendicular lines (rotation of 90 degrees) in terms of rigid transformations.
Two lines can be called parallel if one line can be mapped onto the other by translation.
Two lines can be called perpendicular if one line can be mapped onto the other with a 90 degree rotation. |
PIL 05BEstablish the Corresponding Angles postulate.
If lines are parallel, cut by a transversal, and angles are corresponding, then angles are congruent.
Notice the three pieces of the conditional: parallel, transversal, corresponding. You need all three of these for this postulate to be true, and all three elements must be introduced beforehand in a proof. You can also replace corresponding with any other angle relationship (AIA, AEA, SSI, SSE) and the appropriate conclusion (congruent/ supplementary). |
Constructions (pil 50-55)Construct a right angle.
Construct parallel lines using AIA, Corresponding, Perpendicular to Perpendicular (also two lines parallel to a third are parallel). Construct perpendicular lines through a point off the line. Construct perpendicular lines through a point on the line. Construct rectangle (not a square). Construct a square. See this document shown at right for walkthroughs. |