Question

new vocabulary: • ____: formed when two rays share the same endpoint. the shared endpoint is called the vertex of the angle. • __: two figures (or angles, or line segments) are congruent if they have the same size and shape. for angles, this means they have the same measure. • __ __: when two parallel lines are cut by a transversal, corresponding angles are the angles that occupy the same relative position at each intersection. • __ __: two angles are supplementary if the sum of their measures is 180°. they don’t have to be next to each other, but often are. • __: a line that intersects two or more other lines at different points. • __ __: when two lines intersect, they form pairs of opposite angles called vertical angles. • __ __: coplanar lines that do not intersect. • __ ____: lines that do not intersect and are not coplanar.

Explanation:

1. The first blank: The definition matches that of an "angle" (formed by two rays with a common endpoint, the vertex).
2. The second blank: The description is the definition of "congruent" (same size and shape, for angles same measure).
3. The third blank: The context of parallel lines cut by a transversal and corresponding angles' position refers to "Corresponding Angles".
4. The fourth blank: Angles with a sum of \(180^\circ\) are "Supplementary Angles".
5. The fifth blank: A line intersecting multiple lines at different points is a "Transversal".
6. The sixth and seventh blanks: When two lines intersect, forming opposite angles (vertical angles) is the property of "Vertical Angles" (the term for the angles formed, but the blank here is for the concept of the angles formed, so "Vertical Angles" fits as the pair of angles formed). Wait, re - reading: "When two lines intersect, they form pairs of opposite angles called vertical angles." So the blank is for the angles formed, so "Vertical Angles" (the two - word term for the angles formed).
7. The eighth and ninth blanks: Coplanar non - intersecting lines are "Parallel Lines".
8. The tenth and eleventh blanks: Non - coplanar non - intersecting lines are "Skew Lines".

Answer:

• \(\boldsymbol{\text{Angle}}\): Formed when two rays share the same endpoint. The shared endpoint is called the vertex of the angle.
• \(\boldsymbol{\text{Congruent}}\): Two figures (or angles, or line segments) are congruent if they have the same size and shape. For angles, this means they have the same measure.
• \(\boldsymbol{\text{Corresponding Angles}}\): When two parallel lines are cut by a transversal, corresponding angles are the angles that occupy the same relative position at each intersection.
• \(\boldsymbol{\text{Supplementary Angles}}\): Two angles are supplementary if the sum of their measures is \(180^\circ\). They don't have to be next to each other, but often are.
• \(\boldsymbol{\text{Transversal}}\): A line that intersects two or more other lines at different points.
• \(\boldsymbol{\text{Vertical Angles}}\): When two lines intersect, they form pairs of opposite angles called vertical angles.
• \(\boldsymbol{\text{Parallel Lines}}\): Coplanar lines that do not intersect.
• \(\boldsymbol{\text{Skew Lines}}\): Lines that do not intersect and are not coplanar.