Download Glenbard District 87

Glenbard District 87
Course Title: Geometry
Unit: 1b
Unit Title: Congruence & Proof
Stage 1 – Desired Results
Established Goal(s): What relevant goals (e.g. Content standards, This builds throughout the year – Chapters 2-6, and 9
course or program objectives, learning outcomes, etc.) will this
address?
● Understand congruence in terms of rigid
motions.
● Prove geometric theorems.
● MP: Construct viable arguments and critique
the reasoning of others
Understanding(s): Students will understand that…
● Different types of motions (rigid or dilation)
produce different relationships between
figures
● Geometry has a logical structure based on
proof
● Proofs are required to establish the truth of
mathematical theorems
Essential Question(s): What provocative questions will
foster inquiry, understanding, and transfer of learning?
● What is the relationship between
transformations/motions and the production of
different types of figures?
● Why is proof important?
● What makes a proof valid?
● How does congruence play a role in proofs?
● Why is it important to prove and understand
relationships about lines, angles, parallelograms and
triangles?
Knowledge: Students will know…
Skills: Students will be able to …
G.CO.8 The criteria for triangle congruence (ASA, SAS,
G.CO.6 Use geometric descriptions of rigid motions to transform
SSS, AAS, and HL) follow from the definition of congruence in terms figures and to predict the effect of a given rigid motion on a given
of rigid motions.
figure; given two figures, use the definition of congruence in terms of
rigid motions to decide if they are congruent.
Vocabulary
G.CO.7 Use the definition of congruence in terms of rigid motions to
Isometry/Rigid Motion
show that two triangles are congruent if and only if corresponding
Transversal
pairs of sides and corresponding pairs of angles are congruent.
Alternate Interior/Exterior Angles
G.CO.9 Prove theorems about lines and angles. Theorems include:
Corresponding Angles
vertical angles are congruent; when a transversal crosses parallel lines,
Vertical Angles
alternate interior angles are congruent and corresponding angles are
Linear Pair
congruent; points on a perpendicular bisector of a line segment are
Vertex
exactly those equidistant from the segment’s endpoints.
Isosceles Triangle - Base angles
G.CO.10 Prove theorems about triangles. Theorems include: measures
Consecutive Angles
of interior angles of a triangle sum to 180°; base angles of isosceles
Bisect
triangles are congruent; the segment joining midpoints of two sides of
Medians
a triangle is parallel to the third side and half the length; the medians of
Diagonal
a triangle meet at a point.
Congruent
G.CO.11 Prove theorems about parallelograms. Theorems include:
Adjacent
opposite sides are congruent, opposite angles are congruent, the
Altitude
diagonals of a parallelogram bisect each other, and conversely,
Complementary
rectangles are parallelograms with congruent diagonals.
Supplementary
G.1.2.2 Forms conjectures based on exploring geometric situations with or
Reflexive/Transitive Property
without technology.
Parallel Lines
G.1.2.4 Recognizes flaws or gaps in the reasoning supporting an argument.
G.1.2.5 Formulates and investigates the validity of the converse of a
conditional statement.