Question

if bd is the angle bisector of ∠abc, then \∠abc ≅ ∠abd + ∠dbc\ represents which of the following?
a) transitive property of congruence
b) addition property of equality
c) symmetric property of congruence
d) angle addition postulate
question 14 (5 points)
which of the following is a closed statement?
a) 30 is an odd number.
b) z is a positive number.
c) y is not an odd number.
d) x is an odd number.

Explanation:

First Question (Angle Bisector and Postulate)

The angle addition postulate states that if a point (here, \(D\)) lies in the interior of an angle (\(\angle ABC\)), then the measure of the whole angle is equal to the sum of the measures of the two adjacent angles formed (\(\angle ABD\) and \(\angle DBC\)). The transitive property (A) relates congruence of three figures, the addition property of equality (B) is about equal quantities in equations, and the symmetric property (C) is about reversing congruence. So the angle addition postulate (D) matches \(\angle ABC\cong\angle ABD + \angle DBC\).

Second Question (Closed Statement)

A closed statement (or closed sentence) is a statement that is either true or false, with no variables. Option A ("30 is an odd number") is a false statement but has a definite truth value. Options B, C, and D contain variables (\(z\), \(y\), \(x\)) and their truth values depend on the value of the variable, so they are open statements.

Answer:

D. Angle addition postulate