Question

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

Explanation:

Step1: Analyze the first diagram

The equation $XY + YZ=XZ$ represents the Segment - Addition Postulate. It states that if we have a line segment $XZ$ and a point $Y$ on $XZ$, then the sum of the lengths of the two sub - segments $XY$ and $YZ$ is equal to the length of the whole segment $XZ$. So the answer for the first diagram is A.

Step2: Analyze the second diagram

The second diagram shows a ray splitting an angle into two equal parts, which is the definition of an Angle Bisector. So the answer for the second diagram is B.

Step3: Analyze the third diagram

The equation $AB + BC = AC$ (similar to the first one for segments) represents the Segment - Addition Postulate. So the answer for the third diagram is A.

Step4: Analyze the fourth diagram

The equation $m\angle ABD+m\angle DBC=m\angle ABC$ represents the Angle - Addition Postulate. It states that if we have an angle $\angle ABC$ and a ray $BD$ within $\angle ABC$, then the sum of the measures of the two sub - angles $\angle ABD$ and $\angle DBC$ is equal to the measure of the whole angle $\angle ABC$. So the answer for the fourth diagram is D.

Step5: Analyze the sequence of polygons

The sequence starts with a triangle (3 - sided polygon), then a square (4 - sided polygon), then a pentagon (5 - sided polygon). The pattern is that the number of sides of the polygon increases by 1 each time. The next polygon should have 6 sides, which is a hexagon.

Answer:

First diagram: A. Segment Addition Postulate
Second diagram: B. Angle Bisector
Third diagram: A. Segment Addition Postulate
Fourth diagram: D. Angle Addition Postulate
For the polygon sequence: A. Hexagon (a 6 - sided polygon)