HONORS GEOMETRY 1.5. Angle Relationships Day One.

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Presentation transcript:

HONORS GEOMETRY 1.5. Angle Relationships Day One

Do Now: m<1= 5x+1 m<2 = 2x-12 m<3= 6x-5 m<ABC= 127 Find x

Do Now:

Homework Struggles? Concerns? Confusions? Ask away!!!

Angles Review: Congruent Angles Angle Bisector does what? Four types of angles are …..

Note An angle divides a plane into three distinct parts. Points that lie on the angle Points that lie in the interior of the angle Points that lie in the exterior of the angle

Adjacent Angles Two angles that lie in the same plane and have a common vertex and a common side, but no common interior points.

Vertical Angles Two nonadjacent angles formed by two intersecting lines.

Example One: True/False? <BFD and <CFD are adjacent angles <AFB and <EFD are vertical angles Answer: Name each set of vertical angles? Name three sets of adjacent angles?

Example Two: Which angles are adjacent? Which angles are vertical?

Notice: Vertical angles are always congruent…. Why?

Complementary Angles Two angles whose measure sums to 90 degrees.

Supplementary Angle Two angles whose measures sums to 180 degrees.

Linear Pair Pair of adjacent angles with non-common sides that are opposite rays (i.e. a straight angle. i.e. a line) I.E. Supplementary Angles that are adjacent

Example Three:

You Try!

Ponder…. Are their angles that do not have a complement? Why? Why not?

Example Four: ∠ KPL and ∠ JPL are a linear pair, m ∠ KPL=2x+24, and m ∠ JPL=4x+36. What are the measures of ∠ KPL and ∠ JPL?

Example Five:

You Try!

Perpendicular Lines, segments or rays that form right angles are perpendicular. Notation?

Perpendicular Line Comments

Example Six: AC bisects m ∠ DAB. If ∠ DAC=58, what is m ∠ DAB?

Example Seven:

You Try!

Practice Problems Try some on your own/in small groups As always if you are confuse don’t hesitate to pull me over to ask a question :D Or even better? Ask a tablemate!

Exit Ticket Ray BS bisects <ABC. If m<ABC = 104, what is m<SBC?