Question

name: aaeelah struker date: 9/25/2025 additional geometric terminology n - gen math® geometry there is a great deal of terminology associated with the study of geometry. much of it uses descriptive names that help you understand the idea behind the term. all of this terminology must be mastered for this course. we begin with the concept of a midpoint midpoint of a line segment the midpoint is the unique point on a line segment that divides (or partitions) the line segment into two segments that are the same length (also known as two congruent segments). exercise #1: given $overline{ab}$ shown, do the following: (a) find the length of $overline{ab}$ in centimeters. 8.4 cm (b) based on (a), plot the midpoint of $overline{ab}$ and label it point $m$. (c) make a formal statement about the congruence of two segments:

Explanation:

Step1: Recall mid - point concept

The mid - point divides a line segment into two congruent segments. Given \(AB = 8.4\) cm.

Step2: Calculate mid - point position

The length of \(AM\) and \(MB\) is \(\frac{AB}{2}=\frac{8.4}{2}=4.2\) cm. To plot the mid - point \(M\), measure 4.2 cm from point \(A\) along the line segment \(\overline{AB}\).

Step3: State congruence

Since \(M\) is the mid - point of \(\overline{AB}\), we can say \(\overline{AM}\cong\overline{MB}\).

Answer:

(a) 8.4 cm
(b) Plot point \(M\) 4.2 cm from \(A\) along \(\overline{AB}\)
(c) \(\overline{AM}\cong\overline{MB}\)