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Unit Name:
Triangles
Unit Essential
Question:
Once the triangle congruence criteria (ASA, SSS, AAS, SAS) are established, how can
they be used to prove theorems about triangles and other geometric shapes?
Lesson 1 Vocabulary:
Learning Essential Question 1:
What are the relationships between the interior and
the exterior angles of a triangle and how do these
relationships define a triangle?
Learning Essential Question 2:
How do you justify mathematical statements through
deductive and inductive proofs?
triangle, scalene, isosceles, equilateral, acute,
obtuse, right, equiangular, Theorem: triangle
angle-sum, exterior angle, adjacent-interior
angle, remote-interior angle, Theorems:
exterior-angle, (corollary) exterior angle
inequality, 60º for equilateral triangle, acute
angles of right triangle are complementary
Lesson 2 Vocabulary:
congruent triangles, correspondence,
congruence correspondence, opposite,
included, Postulates: SideSideSide,
SideAngleSide, AngleAngleSide, AngleSideAngle,
flow/paragraph/two-column proof,
CorrespondingPartsCongruentTrianglesCongruent
Learning Essential Question 3:
How do you show sides and angles of triangles are
congruent?
Major Unit Assignment/Assessment
Collins Type 2: Graphic Organizer: Triangle foldable
Analyze, Summarize
Collins Type 3: Two-Column Proof (rewrite, draw, state, PLAN,
DEMONSTRATE)
Written Assessment Quiz Sections 4.1
Collins Type 3: CONGRUENT TRIANGLES 4.2 Two-Column Proof
(rewrite, draw, state, PLAN, DEMONSTRATE)
Written Assessment Test Sections 4.1-4.2
Collins Type 3: CONGRUENT TRIANGLES 4.3 Two-Column Proof
(rewrite, draw, state, PLAN, DEMONSTRATE)
Written Assessment Test Chapter 4
Lesson 3 Vocabulary:
Isosceles Triangle: legs, base, base
angles, vertex angle, Right Triangle:
hypotenuse, leg, locus, altitude, median,
⊥ bisector, concurrent lines, point of
concurrency, centroid (medians),
orthocenter (altitudes), circumcenter (⊥
bisectors), incenter (angle bisectors),
Theorems: Isosceles Triangle Theorem,
Converse Isosceles Triangle Theorem,
Unique Bisector Theorem, LegLegTh,
HypotenuseAngleTh, LegAngleTh, HypotenuseLegTh, TH:
Point is on ⊥ bisector iff equidistant from
endpoints of segment, TH: point is on
angle bisector iff equidistant from sides of
angle, TH: centroid located 2/3 from
vertices to midpoints of opp. sides