Question

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. 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∠ws then which of the following rays is between the other two? a. sw is between sq and su. b. su is between sw and sq. c. sq is between sw and su. d. both a and c e. none of the above 13. 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. if xy bisects 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. if 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:

Step1: Recall transitive property

If \(a = b\) and \(b = c\), then \(a = c\) is the transitive - property, and it states if two quantities are equal to the same quantity, they are equal to each other.

Step2: Analyze angle - betweenness

For the angle \(∠QSU\) with \(m∠QSW = 11\) and \(m∠QSU = 40\), by the definition of betweenness of rays, \(\overrightarrow{SW}\) is between \(\overrightarrow{SQ}\) and \(\overrightarrow{SU}\).

Step3: Analyze collinear - points

For collinear points \(D\), \(G\), and \(K\) with \(KG+KD = GD\), \(K\) is between \(G\) and \(D\).

Step4: Use segment - bisector

If \(\overrightarrow{XY}\) bisects \(\overline{AB}\) at \(M\) and \(AB = 32.8\), then \(MB=\frac{AB}{2}=\frac{32.8}{2}=16.4\).

Step5: Use angle - bisector

If \(\overrightarrow{LO}\) bisects \(∠ALP\) and \(m∠ALO = 59\), then \(m∠ALP = 2\times m∠ALO=2\times59 = 118\).

Answer:

1. E. equal to; Transitive Property
2. A. \(\overrightarrow{SW}\) is between \(\overrightarrow{SQ}\) and \(\overrightarrow{SU}\)
3. C. \(K\) is between \(G\) and \(D\)
4. B. 16.4
5. D. 118