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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

Honors 2.5

Students will prove theorems with perpendicular lines

definitions
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
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
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
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
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.
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