Unit 4: pil-parallel and intersecting lines (using two column proofs)
Pil 01-Use complementary, supplementary, and congruent to compare two angles
Complementary: 2 angles are complementary iff the sum of their measures is 90 degrees
-An angle's complement is an angle that is complementary to the given angle
-∠1 + ∠2 = 90º
-An angle's complement is an angle that is complementary to the given angle
-∠1 + ∠2 = 90º
Supplementary: 2 or more angles are supplementary iff the sum of their measures is 180º
-An angle's supplement is an angle that is supplementary to the given angle
-An angle's supplement is an angle that is supplementary to the given angle
OTHER ADDITIONAL TERMS
*The difference between complementary and supplementary angles, and perpendicular and linear pairs is that complementary angles just have to add to 90 degrees, and perpendicular pairs must add to 90 degrees AND be adjacent. Supplementary angles must add to 180 degrees, but a linear pair must also add to 180 degrees AND be adjacent.
Vertical Angles: Non-adjacent pair of angles formed by 2 intersecting lines.
PIl 02-Given two intersecting lines, identify linear pairs and vertical angles. Use theorems of these angle pairs to solve problems.
Answers
- 24
- 12
- 8
- 24
PIL 03-Prove linear pair theorem |
pil 04-prove vertical angles theorem |
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Pil 05-given 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.
Pil 05a-Define parallel lines (translation) and perpendicular lines (rotation of 90°) in terms of rigid transformations.
Two lines are parallel if one can be mapped onto the other with a translation.
Two lines are perpendicular if one can be mapped onto the other with a 90° rotation.
Two lines are perpendicular if one can be mapped onto the other with a 90° rotation.
pil 05b-Establish the corresponding angles postulate.
Corresponding angles postulate states:
If corresponding angles, formed by transversal across two parallel lines, then angles are congruent.
If corresponding angles, formed by transversal across two parallel lines, then angles are congruent.
pil 06a-Solve problems using parallel lines/transversal theorems (AIA, AEA, SSI, SSE)
If corresponding angles, formed by transversal across two parallel lines, then angles are congruent.
If alternate interior angles, formed by transversal across two parallel lines, then angles are congruent.
If alternate exterior angles, formed by a transversal across two parallel lines, then angles are congruent.
If same side interior angles, formed by a transversal across two parallel lines, then angles are supplementary.
If same side exterior angles, formed by a transversal across two parallel lines, then angles are supplementary.
If alternate interior angles, formed by transversal across two parallel lines, then angles are congruent.
If alternate exterior angles, formed by a transversal across two parallel lines, then angles are congruent.
If same side interior angles, formed by a transversal across two parallel lines, then angles are supplementary.
If same side exterior angles, formed by a transversal across two parallel lines, then angles are supplementary.
pil 06b-Prove four parallel lines transversal theorems (AIA, AEA, SSI, SSE)
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Note: The alternate interior angles and alternate exterior angles, along with the same side interior angles and alternate exterior angles are virtually the same format, so the key only goes over one of each.
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pil 07-use the converse of parallel line/transversal theorems to solve problems.and prove them (Aia, aea, ssi, sse)
Pil 50-55: Constructions
This video I made combines all of the construction skills needed in the PIL unit
PIL 50: Construct a Right Angle
PIL 51a: Construct parallel lines using congruent corresponding angles PIL 51b: Construct parallel lines using congruent AIAs PIL 51c: Construct parallel lines using perpendicular to perpendicular PIL 52: Construct perpendicular lines through a specific point OFF the line PIL 53: Construct perpendicular lines through a specific point ON the line PIL 54: Construct a rectangle that is NOT a square PIL 55: Construct a square |
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This is a document showing what the final results to all the constructions should look like.
PIl unit review
Test your knowledge on everything in this unit
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......And here's the answer key
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