Download Honors Geometry Lesson 1-5: Describe Angle Pair Relationships

Honors Geometry Lesson 1-5: Describe Angle Pair Relationships
Learning Target: By the end of today’s lesson we will be able to successfully solve multi-step problems and
construct proofs involving vertical angles, linear pairs, and supplementary angles.
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Two angles are ______________________ if the sum of their angle measure is 90˚.
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Two angles are ______________________ if the sum of their angle measures is 180˚.
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Each angle is the _________________ of each other.
Each angle is the ________________ of each other.
_________________ are two angles that share a common vertex and side, but have no common interior
points.
Example 1:
a.) In the figure, name a pair of complementary angles,
a pair of supplementary angles, and a pair of adjacent angles.
b.) Are BDE and CDE adjacent angles? Explain why or why not.
Example 2:
a.) Given that 1 is a complement of 2 and m2 = 57°, find m1.
b.) Given that 3 is a supplement of 4 and m4 = 41°, find m3.
Example 3:
The basketball pole forms a pair of supplementary angles with the ground.
Find mBCA and mDCA.
Example 4: Find mABC and mCBD.
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Two adjacent angles are a _______________ if their non-common sides are opposite rays.
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Two angles are _________________ if their sides form two pairs of opposite rays.
Example 7:
a.) Identify all of the linear pairs and all of the vertical angles in the figure below.
b.) Are 1 and 4 a linear pair? Explain why or why not.
Example 8:
a.) Two angles form a linear pair. The measure of one angle is 4 times the measure of the
other. Find the measure of each angle.
b.) The measure of an angle is twice the measure of its complement. Find the measure of
each angle.
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There are some things you can conclude from a diagram,
and some you cannot. From the below you CAN conclude.
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All points shown are __________________.
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Points A, B, and C are ______________, and
B is between A and C.
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AC, BD, BE _________________________, at
point B.
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DBE and EBC are _________________ angles,
and ABC is a ______________________.
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Point E lies in the __________________ of DBC.
From the diagram below you
CANNOT conclude.
AB  BC
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DBE  EBC
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ABD is a right angle.
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This information must be
indicated, as shown below.