Question

1. (a) is the following sentence true? according to betweenness of points, if points a, b, and c are collinear and ab + bc = ac then c is between a and b. a. yes b. no c. maybe d. sometimes e. not applicable 2. (19) two rays joined together so that they have the same endpoint make a(n) __ a. angle b. square c. circle d. triangle e. none of the above 3. (112) the midpoint of a line segment is the point that divides the line segment into congruent line segments. a. five b. three c. four d. two e. not applicable 4. (111) a(n) angle is an angle with a measure of less than 90 degrees. a. right b. obtuse c. acute d. straight e. congruent 5. (110) if point s lies in the interior of ∠qpr, and m∠spr + m∠qps = __, then (overrightarrow{ps}) is between (overrightarrow{pq}) and (overrightarrow{pr}). a. m∠qsr b. m∠qpr c. m∠sqr d. m∠srp e. m∠srq

Explanation:

1. For the first question, the correct between - ness property requires \(AB + BC=AC\) for \(B\) to be between \(A\) and \(C\). The statement in the question is incorrect as it is not in the proper form of the between - ness property.
2. By definition, two rays with the same endpoint form an angle.
3. The mid - point of a line segment divides it into two congruent line segments.
4. An acute angle is defined as an angle with a measure less than 90 degrees.
5. If a point \(S\) lies in the interior of \(\angle QPR\), then \(m\angle SPR + m\angle QPS=m\angle QPR\) according to the angle - addition postulate.

Answer:

1. B. No
2. A. angle
3. D. two
4. C. acute
5. B. \(m\angle QPR\)