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Geometry
Chapter 6: Congruent Triangles
6.1.1: Congruent Triangles
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Learning Target:
n I
can identify congruent triangles by
determining that the triangles are similar
and have a similarity ratio of 1.
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Mathematical Practice:
n Construct
viable arguments and critique
the reasoning of others.
n Mathematically
proficient students
understand and use stated assumptions,
definitions, and previously established
results in constructing arguments.
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CCSSM:
n Understand
similarity in terms of
similarity transformations.
n Given
two figures, use the definition of
similarity in terms of similarity
transformations to decide if the figures are
similar.
n Explain using similarity transformations the
meaning of similarity for triangles as the
equality of all corresponding pairs of
angles and the proportionality of all
corresponding pairs of sides.
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CCSSM:
n Understand
congruence in terms of
rigid motions.
n Given
two figures, use the definition of
congruence in terms of rigid motion to
decide if the figures are congruent.
n Use the definition of congruence in terms of
rigid motions to show that two triangles are
congruent if and only if corresponding
pairs of sides and corresponding pairs of
angles are congruent.
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CCSSM:
n Understand
congruence in terms of
rigid motions.
n Explain
how the criteria for triangle
congruence (ASA, SAS, and SSS) follow from
the definition of congruence in terms of
rigid motions.
n Use congruence and similarity criteria for
triangles to solve problems and prove
relationships between geometric figures.
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Quote for today:
n “Geometry
enlightens the intellect and
sets one’s mind right.”
n Ibn
Khaldun (1332 – 1406)
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Similar Figures & Triangle
Similarity Conditions:
n Similar
figures are shapes that have the
same shape. Corresponding angles have
the same measure.
n Triangle
n AA~
n SAS~
n SSS~
Similarity Conditions:
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Rigid Transformations:
n Reflections
n Translations
n Rotations
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Congruent Shapes:
n Two
figures are congruent if and
only if:
n they
have the same shape and the same
size.
n there is a sequence of rigid
transformations that carry one figure
onto the other.
n they are similar and their similarity
ratio is 1.
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Assignments:
n CW
6.1.1: Problems 6-1 through 6-3.
n HW
6.1.1: Problems 6-4 through 6-10.