Congruent Segments: A Review

Congruent Segments: A Review Section 2-3 Fellow: Brooke Odle Teacher: Ms. Sanchez Subject: Math- Geometry(10th grade) School: Saint Vincent Academy Date: October 13, 2011

Objectives • Understand key vocabulary words mentioned in Section 2-3: • Congruent Segments • Theorem • Midpoint • Bisect • Integrate “Algodoo” to reinforce understanding of vocabulary • Identify congruent segments and determine their midpoints • Demonstrate how bisecting a congruent segment at its midpoint yields two congruent segments • Real-world application of Congruent Segments • Biomechanics and anthropometric measures

Let’s Review! • How do you know if two segments are congruent? • Two segments are congruent if and only if they have the same length • What is a theorem? • A theorem is a statement that can be justified by using logical reasoning. Congruence is related to the equality of segment measures, so there are properties of congruence that are similar to the corresponding properties of equalities.

Algodoo Scene Demonstration • Algodoo is a two-dimensional physics-based simulation software. • In the following Algodoo scene, which segments are congruent segments? • Express with Theorems 2-1, 2-2, 2-3 • Hint: • Theorem 2-1: Congruence of segments is reflexive • Theorem 2-2: Congruence of segments is symmetric • Theorem 2-3: Congruence of segments is transitive

Let’s Review! • What is a midpoint? • A midpoint is a unique point on a segment at which the segment can be separated into two segments of equal length. The resulting two segments are congruent segments.

Algodoo Scene Demonstration: Part II • Now that we have identified the congruent segments in the Algodoo scene, let’s identify the midpoints of the segments

Let’s Review! • What does it mean to bisect something? • When we bisect something, we separate it into two equal parts. • The midpoint of a segment bisects the segment because it separates the segment into two congruent segments.

Algodoo Scene Demonstration: Part III • Now that we have identified the congruent segments and their respective midpoints, what will happen if we bisect the segments at their midpoint? • Use the cut tool in Algodoo

Real-world Application of Congruent Segments • Biomechanics involves the application of mechanical principles to biological systems, like humans, animals, plants, organs, and cells. • Biomechanics of human movement is an interdisciplinary field: • Engineering, Kinesiology, Exercise Science, Athletic Training, Ergonomics, Physical and Occupational Therapy, etc…

Real-world Application of Congruent Segments • When human movement biomechanists want to understand movement, they need to collect anthropometric measures • Anthropometry is a branch of anthropology that studies the physical measurements of the human body to determine differences in individuals and groups. • Measures include race, sex, age, and body type • Anthropometric charts can be used to determine body segment lengths (length between joints)

AnthropometRic Chart Body segment lengths are a fraction of body height H. Based on this chart, are any body parts congruent segments? (Hint: Hold out your hands; Stand up) Anthropometric charts are not perfect- good approximations when you can’t measure individual directly http://www.mech.utah.edu/ergo/pages/Educational/safety_modules/ctd-anthropometry/index.html

Screenshot of algodoo scene Algodoo Scene with segments: Students were asked which segments were congruent. To reinforce that students need to have a number line or measurement system to determine whether segments are congruent, the ruler feature was not selected for each segment until the students realized they had no accurate way to measure the segments. Once the ruler feature was added for each segment, the students identified the congruent segments and used the ruler to determine the midpoint.

Screenshot of algodoo scene This scene shows how the students identified the midpoint of one of the congruent segments and bisected the segment, using the cut tool, to reveal two congruent segments. The tick marks on the segments are indicative of the ruler feature being enabled.,

Congruent Segments: A Review