Question

1. (1) 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. (10) 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 then which of the following rays is between the other two? a. sw⃗ is between sq⃗ and su⃗. b. su⃗ is between sw⃗ and sq⃗. c. sq⃗ is between sw⃗ and su⃗. d. both a and c e. none of the above 13. (8) 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 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. (12) if xy⃡ bisects ab̅ at point m, and ab = 32.8, then find mb. (hint: use the definition an angle bisector.) a. 17.8 b. 16.4 c. 15.3 d. 11.1 e. none of the above 15. (12) if lo⃗ 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 if two quantities are equal to the same quantity, they are equal to each other.

If point \(W\) lies in the interior of \(\angle QSU\) and \(m\angle QSW = 11\), \(m\angle QSU=40\), then \(\overrightarrow{SW}\) is between \(\overrightarrow{SQ}\) and \(\overrightarrow{SU}\) based on the definition of between - ness of rays in an angle.

If points \(D\), \(G\), and \(K\) are collinear and \(KG + KD=GD\), by the segment - addition postulate (a key concept in the between - ness of points on a line), \(K\) is between \(G\) and \(D\).

Answer:

E. equal to; Transitive Property

12.