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Honors 2.5. Students will prove theorems with perpendicular lines. Definitions. Perpendicular lines are 2 lines that intersect to form 4 right angles. the definition can be used as follows If JK is perpendicular ( ) to MN (written as JK MN), then the numbered angle is a right angle.
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Honors 2.5 Students will prove theorems with perpendicular lines
Definitions • Perpendicular lines are 2 lines that intersect to form 4 right angles. • the definition can be used as follows • If JK is perpendicular () to MN (written as JK MN), then the numbered angle is a right angle. • Converse which is ________________
Theorems • Thm 2-4 If 2 lines are , then they form congruent adjacent () angles. • Thm. 2-5 If 2 lines form congruent adjacent angles, then the lines are perpendicular. • Thm. 2-6 If the exterior sides of 2 adjacent acute angles are , then the angles are complementary.
Try this • AB CD. Use the diagram to classify each statement as true or false. • AB EF • CGB is a right angle • CGA is a right angle • m DBG = 90 • EGC and EGA are complements • DGF is complementary to DGA • EGA is complementary to DGF A E C D G F B
Practice Always, Sometimes, Never • The length of a segment is ____ negative. • A bisector of a segment is ___ a line. • A ray ____ has a midpoint. • AB and BA _____ denote the same ray. • Two intersecting lines ___ lie in exactly one plane. • When A and B are in a plane, AB is ____ in the plane.
Always, Sometimes, Never • Perpendicular lines ____ lie in the same plane. • Two lines are perpendicular iff they __ form congruent adjacent angles. • If the exterior sides of 2 adjacent angles are perpendicular, then the angles are __ supplementary. • If a pair of vertical angles are supplementary, the lines forming the angles are __ perpendicular.
