Question

1. determine which definition, property, or postulate is represented by each diagram. write the letter of the correct item in the box. a. segment addition postulate d. angle addition postulate b. angle bisector e. segment bisector c. midpoint f. vertical angles yz = xz m∠abd + m∠dbc = m∠abc next figure in the following sequence.

Explanation:

Step 1: Analyze first - type of problem

For the part of matching diagrams with definitions:

• If a diagram shows a point dividing a segment into two equal parts, it represents a mid - point (C). But we don't have enough information about the first diagram to determine it precisely from the given text in the question.
• For the diagram with a ray splitting an angle into two equal angles, it represents an angle bisector (B).
• For the diagram where the sum of two adjacent angles equals a larger angle ($m\angle ABD + m\angle DBC=m\angle ABC$), it represents the angle addition postulate (D).

Step 2: Analyze second - type of problem

For the sequence of figures (triangle, square, pentagon, hexagon), the pattern is that the number of sides of the polygon is increasing by 1 each time. So the next figure should be a heptagon (a 7 - sided polygon). But since we don't have options for the heptagon in the visible part of the question for the sequence part, we focus on the first part of matching with given options.

Answer:

For the matching part (assuming we are only considering the parts with enough information):

• Second diagram: B. Angle Bisector
• Third diagram: D. Angle Addition Postulate