|
Triangles and Congruence
In this unit, students continue to use constructions to
explore attributes of geometric figures along with
congruence transformations to make conjectures and
justify properties of geometric figures. They will
justify and apply triangle congruence relationships and
make and verify conjectures about angles of triangles
choosing from a variety of approaches such as
coordinate, transformational, or axiomatic. Students
will also be exploring numeric and geometric patterns to
make generalizations about geometric properties and
angle relationships. When students report, they will
generate or extend a pictorial model, a symbolic
representation or a graphical representation from a
verbal description, or a graphical representation from a
symbolic representation in order to solve problems.(15
days)
Critical Questions
Can you draw a triangle that does not have an interior sum of 180
degrees?
How is congruent different than equal?
What makes some triangles special?
What are the special lines of a triangle?
|
| |
|
|
|
Student Performance Expectations |
|
Key
Information in the brackets that is not in bold (8.2A) is the
Texas Essential Knowledge and Skill (TEKS) that this objective
is aligned to.
Information in
the brackets that is in bold
(8.2.11B) (8.2.12A)
(11.2US10A)
is the specific Texas Assessment of Knowledge and Skills (TAKS-
test) objective this objective is aligned to. |
|
Use constructions to explore attributes of geometric figures
and to make conjectures about geometric relationships.
(G.2A) |
|
Make conjectures about angles, lines, polygons, circles, and
three-dimensional figures and determine the validity of the
conjectures, choosing from a variety of approaches such as
coordinate, transformational, or axiomatic. (G.2B) |
|
Use logical reasoning to prove statements are true
and find counter examples to disprove statements that are
false. (G.3C) |
|
Use numeric and geometric patterns to make
generalizations about geometric properties, including properties
of polygons, ratios in similar figures and solids, and angle
relationships in polygons and circles. (G.5B) (T 11) |
|
Use slopes and equations of lines to investigate
geometric relationships, including parallel lines, perpendicular
lines, and special segments of triangles and other polygons.
(G.7B) (T 11) |
|
Formulate and test conjectures about the properties
of parallel and perpendicular lines based on explorations and
concrete models. (G.9A) |
|
Formulate and test conjectures about the properties
and attributes of polygons and their component parts based on
explorations and concrete models. (G.9B) |
