Final Answer:
- Supplementary angles: ∠a and ∠b are supplementary angles if the sum of their measures is equal to 180°.
- Vertical angles: ∠c and ∠d are vertical angles if they share the same vertex and their sides form two pairs of opposite rays.
- Complementary angles: ∠e and ∠f are complementary angles if the sum of their measures is equal to 90°.
Step-by-step explanation:
When a transversal intersects two lines, it creates various angle relationships. Firstly, for supplementary angles (∠a and ∠b), their measures add up to 180°. Mathematically, this is expressed as ∠a + ∠b = 180°. This relationship is a fundamental property that emerges when two parallel lines are intersected by a transversal. It signifies that the angles are positioned in a way that their combined measure results in a straight line.
Next, vertical angles (∠c and ∠d) are formed when two lines intersect, and their sides form pairs of opposite rays. These angles are congruent, meaning they have equal measures. Symbolically, if ∠c is the measure of one vertical angle, then ∠d has the same measure. This property is crucial in understanding the symmetry created by the intersection of lines.
Finally, complementary angles (∠e and ∠f) have measures that sum up to 90°. In mathematical terms, ∠e + ∠f = 90°. When a transversal intersects two lines, creating a right angle, the angles on either side of the transversal become complementary. This concept is vital in understanding how certain angles work together to form specific geometric configurations.