Logic & Proofs

What type of angles are formed by the same 2 lines and share a point of intersection known as their vertex?

• Horizontal Angles

• Supplementary Angles

• Corresponding Angles

• Vertical Angles

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

Identify the converse. (HInt: switch the hypothesis & conclusion)

• 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.

Use the law of syllogism (like cause & effect) to draw a conclusion from the two given statements:

Statement 1: If you exercise regularly, then you have a healthy body

Statement 2: If you have a healthy body, then you have more energy

• You have more energy

• If you exercise regularly, then you have more energy

• You have a healthy body

• If you do not have a healthy body, then you do not exercise regularly

Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.

• Inductive

• Deductive

Reasoning based on specific examples and patterns used to form conjectures is called ______________ reasoning.

• Inductive

• Deductive

Which is given in the diagram?

• BD ≅ BD
• AB ≅ BC
• D is the midpoint of AC
• ΔABD ≅ ΔCBD

Which is NOT given in the diagram?

• AC ≅ EC
• BC ≅ DC
• AB ≅ ED
• All of these are given

Tags

CCSS.HSG.SRT.B.5

What does the word BISECT mean?

• To cut something into 2 pieces or non-congruent parts.

• It is a plane containing a coordinate plane, x-axis & y-axis.

• A shape that has two or more sides cut into pieces.

• To cut something into 2 congruent pieces or exactly in half.

Which Postulate/Definition would you use to find HG?

• Segment Addition Postulate

• Angle Addition Postulate

• Definition of Segment Bisector

• Definition of Angle Bisector

Which of the following theorems/postulates would verify that ∠COB & ∠AOD are congruent?

• Straight Angle Theorem

• Congruent Compliments Theorem

• Vertical Angles Theorem

• Linear Pair Theorem