Logic and Reasoning in Geometry

• Conditional Statement
• Inverse
• Converse
• THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

• Conditional 
• Converse
• Inverse
• Contrapositive

Consider the conditional statement.

"If a triangle is equiangular, then it is also equilateral"

Identify the hypothesis A.

Identify the conclusion B.

Groups:

(a) Hypothesis A

,

(b) Conclusion B

• a triangle is equiangular

• it is also equilateral

Which of the following statements is logically equivalent to "If it is raining, then the ground is wet"?

• If the ground is not wet, then it is not raining.

• If the ground is wet, then it is raining.

• If it is not raining, then the ground is not wet.

• If the ground is not wet, then it is raining.

Tags

TEKS.MATH.9-12.VIII.B

What is the contrapositive of the statement "If a figure is a square, then it has four sides"?

• If a figure has four sides, then it is a square.

• If a figure is not a square, then it does not have four sides.

• If a figure does not have four sides, then it is not a square.

• If a figure is a square, then it does not have four sides.

Tags

TEKS.MATH.9-12.VIII.B

Given, "If angles are congruent, then the measures of the angles are equal." Identify the contrapositive.

• If the measures of the angles are equal, then the angles are congruent.
• If angles are not congruent, then the measures of the angles are not equal.
• If the measures of the angles are not equal, then the angles are not congruent.
• If the angles are not congruent, then the measure of the angles are equal.

Tags

CCSS.HSG.SRT.B.5

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid."

What is the contrapositive of this statement?

• If a polygon is a trapezoid, then it is a quadrilateral.

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• A rectangle is also a quadrilateral.

What is a counterexample of the statement below?

"If an animal has wings, then it can fly."

• Duck

• Penguin

• Rabbit

• Snake

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

For the inverse we _________ the hypothesis and conclusion

• switch
• negate
• switch and negate

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.

• If I do not have a Siberian Husky, then I do not have a dog.
• If I have a dog, then I have a Siberian Husky.
• If I do not have a dog, then I do not have a Siberian Husky.
• If I do not have a Siberian Husky, then I have a dog. 

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A