Question

describe each postulate in your own words.
1 linear pair postulate
2 segment addition postulate
3 angle addition postulate
remember
a conditional statement is a statement in the form \if p, then q.\ you read the expression ( p
ightarrow q ) as \p implies q.\
the variable p represents the hypothesis, and the variable q represents the conclusion.
you can accept a postulate without proof, but you must prove that a theorem is true.
practice
1 complete a truth table for the conditional statements.
a if ( angle 1 ) and ( angle 2 ) are vertical angles, then ( angle 1 cong angle 2 ).
b if ( m angle 1 = 100 ^ { circ } ), then ( angle 1 ) is an obtuse angle.

Explanation:

Step1: Understand the truth - value rules for \(p

ightarrow q\)
The conditional statement \(p
ightarrow q\) is false when \(p\) is true and \(q\) is false. Otherwise, it is true.

Step2: Analyze part (a)

• When \(p\) ( \(\angle1\) and \(\angle2\) are vertical angles) is True:
• If \(q\) (\(\angle1\cong\angle2\)) is True, then \(p

ightarrow q\) is True.

• If \(q\) (\(\angle1\cong\angle2\)) is False, then \(p

ightarrow q\) is False.

• When \(p\) ( \(\angle1\) and \(\angle2\) are vertical angles) is False:
• Whether \(q\) (\(\angle1\cong\angle2\)) is True or False, \(p

ightarrow q\) is True.

Step3: Analyze part (b)

• When \(p\) (\(m\angle1 = 100^{\circ}\)) is True:
• If \(q\) (\(\angle1\) is an obtuse angle) is True (since an angle with measure \(100^{\circ}\) is obtuse, \(q\) is True), then \(p

ightarrow q\) is True.

• If \(q\) (\(\angle1\) is an obtuse angle) is False (which is not the case here as \(100^{\circ}>90^{\circ}\)), then \(p

ightarrow q\) is False.

• When \(p\) (\(m\angle1 = 100^{\circ}\)) is False:
• Whether \(q\) (\(\angle1\) is an obtuse angle) is True or False, \(p

ightarrow q\) is True.

Answer:

For part (a):

\(p\) (\(\angle1\) and \(\angle2\) are vertical angles)

\(q\) (\(\angle1\cong\angle2\))

\(p

ightarrow q\) |

True	True	True
True	False	False
False	True	True
False	False	True

For part (b):

\(p\) (\(m\angle1 = 100^{\circ}\))

\(q\) (\(\angle1\) is an obtuse angle)

\(p

ightarrow q\) |

True	True	True
True	False	False
False	True	True
False	False	True