3.6 prove theorems about perpendicular lines. foldable
TRANSCRIPT
3.6Prove
Theorems About
Perpendicular Lines
Foldable
Thms.Thm 3.8If 2 lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Thm 3.9If 2 lines are perpendicular, then they intersect to form 4 rightangles.
Thms.Thm 3.10If 2 sides of 2 adj. acute angles are perpendicular, then the angles are complementary.
Thm 3.11 Perpendicular Transversal ThmIf a transversal is perpendicular to 1 of 2 // lines, then it is perpendicular to the other.
Thms.Thm 3.12 Lines perpendicular to a TransversalIn a plane, if 2 lines are perpendicular to the same line, then they are // to each other.
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Distance from a point to a line: The length of the perpendicular segment from the point to the line
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1. Given
€
PS⊥PQ
Thm 3.10
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Given
Thm 3.8
Thm 3.9
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r and s are both perpendicular to x, so by Thm 3.12 r//s. x and y are both perpendicular to r, so byThm 3.12 x//y. x and z are both perpendicular to s,so x//z. y and z are both // to x, by the transitiveProperty of // lines y//z.
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