Question

1. (l13) complete the following sentence and determine the property being described: if two quantities are ____ the same quantity, then they are equal to each other. if a = b and b = c, then a = c. a. substituted for; substitution property b. substituted for; transitive property c. equal to; reflexive property d. subtracted from; subtraction property e. equal to; transitive property 12. (l10) use betweenness of points or rays to answer the following question: if point w lies in the interior of ∠qsu, m∠qsw = 11, m∠qsu = 40, and m∠wsu = 29. then which of the following rays is between the other two? a. $overrightarrow{sw}$ is between $overrightarrow{sq}$ and $overrightarrow{su}$. b. $overrightarrow{su}$ is between $overrightarrow{sw}$ and $overrightarrow{sq}$. c. $overrightarrow{sq}$ is between $overrightarrow{sw}$ and $overrightarrow{su}$. d. both a and c e. none of the above 13. (l8) use betweenness of points or rays to answer the following question: if points d, g, and k are collinear and kg + kd = gd, then which point is between the other two? a. g is between k and d. b. d is between k and g. c. k is between g and d. d. both a and c e. none of the above 14. (l12) if $overrightarrow{xy}$ bisects $overline{ab}$ at point m, and ab = 32.8, then find mb. (hint: use the definition of an angle bisector.) a. 17.8 b. 16.4 c. 15.3 d. 11.1 e. none of the above 15. (l12) if $overrightarrow{lo}$ bisects ∠alp, and m∠alo = 59, then find m∠alp. a. 90 b. 45 c. 124 d. 118 e. none of the above

Explanation:

11.

The transitive property of equality states that if \(a = b\) and \(b = c\), then \(a = c\), which means two quantities equal to the same quantity are equal to each other.

The measure of an angle is the sum of the measures of its non - overlapping sub - angles. Given \(m\angle QSU=40\), \(m\angle QSW = 11\) and \(m\angle WSU=29\), and since \(m\angle QSW+m\angle WSU=m\angle QSU\), ray \(\overrightarrow{SW}\) is between \(\overrightarrow{SQ}\) and \(\overrightarrow{SU}\).

If three collinear points \(D\), \(G\), and \(K\) satisfy \(KG + KD=GD\), by the segment - addition postulate, point \(K\) is between \(G\) and \(D\).

Answer:

E. equal to; Transitive Property

12.