Congruent Segments: A Review

Fellow: Brooke Odle
Teacher: Ms. Sanchez
Subject: Math- Geometry(10th grade)
School: Saint Vincent Academy
Date: October 13, 2011

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

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 is a two-dimensional physicsbased 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

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.

Now that we have identified the
congruent segments in the Algodoo
scene, let’s identify the midpoints of the
segments

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.

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
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…

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)
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
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.
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.,
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