Question

1. a right - angle is an angle with a measure of a. greater than 90 but less than 180 b. greater than 90 c. greater than 0 but less than 90 d. 90 e. less than 90
2. points are points that do not lie on the same line. a. end b. collinear c. unequal d. noncollinear e. coordinate
3. the rays of an angle are called the angle’s a. end points b. sides c. vertex d. union e. line segments

from each given statement below, select the definition, property, or postulate that justifies the prove statement.

1. given: ∠aoc, b which lies in the interior of ∠aoc, and m∠aob = m∠boc prove: ob bisects ∠aoc. a. substitution property b. definition of a segment bisector c. reflexive property d. betweenness of rays e. definition of an angle bisector
2. given: 3pq = 3st prove: pq = st a. addition property b. reflexive property c. division property d. symmetric property e. definition of a segment bisector
3. given: jk + kr = jr prove: jk = jr - kr a. subtraction property b. transitive property c. multiplication property d. substitution property e. definition of a segment bisector
4. given: 1/2m∠efg = m∠2 and m∠2 = 1/2m∠jkl prove: m∠efg = m∠jkl a. substitution property; addition property b. reflexive property; division property c. betweenness of rays d. definition of an angle bisector e. transitive property; multiplication property

select the answer to each problem below using the figure below.

1. which of the following choices gives the names of the six line segments in the figure? a. gki, hki, ikg, ghi, hik, gik b. g, h, i, k, hi, hg c. hi, hk, gi, gh, gk, ik d. gh, ghi, ih, ihg, kg, ki e. gk, hk, ik, gh, hi, gi
2. choose the angles in the figure that can be named with just one letter. a. ∠h, ∠k b. ∠g, ∠i c. ∠k, ∠i d. ∠g, ∠k e. ∠h, ∠i

Explanation:

1. A right - angle is defined as an angle with a measure of 90 degrees.
2. Points that do not lie on the same line are non - collinear.
3. The rays of an angle are called the angle's sides.
4. If a ray divides an angle into two equal angles, it is the angle bisector by definition.
5. Given \(3PQ = 3ST\), dividing both sides by 3 (Division Property) gives \(PQ=ST\).
6. Given \(JK + KR=JR\), subtracting \(KR\) from both sides (Subtraction Property) gives \(JK = JR - KR\).
7. Given \(\frac{1}{2}m\angle EFG=m\angle2\) and \(m\angle2=\frac{1}{2}m\angle JKL\), by the Transitive Property and multiplying both sides by 2 (Multiplication Property), we can prove \(m\angle EFG = m\angle JKL\).
8. The six line segments in the triangle are \(\overline{GK},\overline{HK},\overline{IK},\overline{GH},\overline{HI},\overline{GI}\).
9. In the triangle, the angles that can be named with one letter are \(\angle G\) and \(\angle I\) since they are the only angles at those vertices.

Answer:

1. D. 90
2. D. Noncollinear
3. B. sides
4. E. Definition of an angle bisector
5. C. Division Property
6. A. Subtraction Property
7. E. Transitive Property; Multiplication Property
8. E. \(\overline{GK},\overline{HK},\overline{IK},\overline{GH},\overline{HI},\overline{GI}\)
9. B. \(\angle G,\angle I\)