Question

1. ruler postulate
2. protractor postulate

state whether each statement is a conditional, a conjunction, a disjunction, or a biconditional. then determine whether it is true or false. 1.5, 2.2 - 2.3

1. |c| = c if c ≥ 0 and |c|=-c if c < 0.
2. if ba = bc, b is the mid - point of $overline{ac}$.
3. if ∠c is a straight angle, m∠c = 90°.
4. ∠1≅∠2 if and only if m∠1 = m∠2.
5. if ∠bac and ∠cad are adjacent angles, then m∠bac + m∠cad = m∠bad.

review the properties of equality. what would each property of inequality be? 2.5

1. addition property for ≥
2. reflexive property for ≥
3. transitive property for ≥

Explanation:

50.

Step1: Identify the statement type

The statement has two parts joined by "and", so it is a conjunction.

Step2: Check truth - value

The definition of the absolute - value function \(|c|=

$$\begin{cases}c, & c\geq0\\-c, & c < 0\end{cases}$$

\) is correct. So the statement is true.

Step1: Identify the statement type

The statement has the form "If... then...", so it is a conditional.

Step2: Check truth - value

Just because \(BA = BC\), \(B\) is not necessarily the mid - point of \(\overline{AC}\). For \(B\) to be the mid - point of \(\overline{AC}\), \(BA=BC\) and \(B\) must lie on \(\overline{AC}\). So the statement is false.

Step1: Identify the statement type

The statement has the form "If... then...", so it is a conditional.

Step2: Check truth - value

A straight angle has a measure of \(180^{\circ}\), not \(90^{\circ}\). So the statement is false.

Answer:

Conjunction, True

51.