Geometry B
Name:______________________
Date: ___________
Chapter 6: Polygons and Quadrilaterals
Section 6.5: Conditions for Special Parallelograms
DO NOW
ABCD is a parallelogram. Justify each statement.
1. ABC  CDA
2. AEB  CED
Simplify
3. √625
4. √124
Objectives of Lesson: ________________________________________
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When would I ever use this? Building contractors and carpenters can use the
conditions for rectangles to make sure the frame for a house has the
correct shape.
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Conditions for Rectangles
Theorem
Example
2
Example 1: Carpentry Application
A manufacture builds a mold for a desktop so that
, and mABC = 90°. Why must ABCD be a rectangle?
Example 2: Carpentry:
A contractor built a wood frame for the side of a house so that XY ≅ WZ
and XW ≅ YZ . Using a tape measure, the contractor
found that XZ = WY. Why must the frame be a rectangle?
Example 3: Carpentry: A carpenter’s square can be used to test that an angle
is a right angle. How could the contractor use a carpenter’s square to check
that the frame is a rectangle?
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3
Conditions for Rhombi
Theorem
Example
Caution___________________________________________________
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Remember_________________________________________________
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Example 3: Applying Conditions for Special Parallelograms
Determine if the conclusion is valid. If not, tell what additional information
is needed to make it valid.
4
Example 4: Applying Conditions for Special Parallelograms
Example 5
Determine if the conclusion is valid. If not, tell what additional information
is needed to make it valid.