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Geometry Worksheet 2.3
Laws of Syllogism, Detachment, and Venn diagrams
Name _______________________
Per ___ Date _________________
For problems 1-3, use the conditional statement below.
Given: If two angles measure 45 and 135 degrees, then they are supplementary.
1.
Draw a Venn diagram of the conditional statement.
2. Given: Angle A is 45 degrees and Angle B is 135 degrees.
Conjecture:
Why is it true?
3.
Given: Angle C and Angle D are supplementary.
Conjecture:
Why is it true?
For problems 4-6, use the conditional statements below.
Given: If two angles measure 30 and 60 degrees, then the sum of their measures is 90 degrees.
If the sum of the measures of two angles is 90 degrees, then they are complementary.
4.
Conjecture: If two angles are complementary, then they measure 30 and 60 degrees.
True or False?
Why?
5.
Conjecture: If two angles measure 30 and 60 degrees, then they are complementary.
True or False?
Why?
6.
Conjecture: If the sum of two angles is 90 degrees, then they measure 30 and 60 degrees.
True or False?
Why?
For problems 7-11, Use the givens provided to write your own conjecture. If no conjecture can be made, write
NONE. Justify your answer for each.
7.
Given: If it snows outside, you will wear your winter coat.
It is snowing outside.
Conjecture:
Justification:
8.
Given: If two angles are complementary then they are both acute angles.
Angles 1 and 2 are acute angles.
Conjecture:
Justification:
9.
Given: If you enjoy reading, then you read books.
If you are in 10th grade, then you passed 9th grade.
Conjecture:
Justification:
10. Given: If it rains, then the field will be muddy.
If the field is muddy, then the game will be canceled.
Conjecture:
Justification:
11. Given: If it snows, then it is below 33 degrees.
If it is below 33 degrees, then you should wear a coat.
Conjecture:
Justification:
Draw a Venn diagram for each:
12. If a number is a whole number, then it is an integer.
13. If a number is an integer, then it is a rational number.
14. If a number is a rational number, then it is a real number.
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