Honors 2.5

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# Honors 2.5 - PowerPoint PPT Presentation

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.