Download Unit 6 Congruent Triangles Objectives

Unit 5: Triangle Relationships
Pacing: 4 weeks
Unit Overview
The triangle relationships unit has two major themes. First, students apply properties of triangles to
solve problems about angles and sides. Second, students use relationships of corresponding parts of
two triangles to test for triangle congruence. Constructions are used as a way to explore properties of
triangles. Throughout the unit, students may be asked to construct proofs about triangles.
Essential Ideas
1. Understand and apply theorems about triangles.
2. Use the SSS, SAS, ASA and AAS postulates to test for triangle congruence.
3. Use coordinates to prove simple geometric theorems algebraically.
Required Common Assessments
District summative assessments in which students demonstrate their understanding of the content and skills
they have acquired during this unit. Assessments are directly aligned to standards and expectations.
Lesson Sequence and Objectives
objective
MMS
Optional review: Classify triangles by angles and sides.
Determine if a triangle can exist based on the side
lengths.
4.G.A.2
5.G.B
7.G.A.2
Understand and apply theorems about
triangles. Theorems include: measures of interior angles
of a triangle sum to 180°; base angles of isosceles
triangles are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side and half
the length.
7.G.B.5
8.G.A.5
Optional: The medians of a triangle meet at a point.
Solve multistep problems involving angle measure and
side length in triangles, with an emphasis on problems in
which angles measure or side length is written as a
variable expression.
Name and label corresponding parts of congruent
triangles.
Use transformations to justify congruence.
Use the SSS, SAS, ASA and AAS postulates to test for
triangle congruence. Hypotenuse-Leg is recommended.
Write proofs about congruent triangles.
Given the coordinates of the vertices of a triangle,
determine the coordinates of the other vertices. Include
problems in which coordinates are variables.
Use coordinates to prove simple geometric theorems
algebraically. For example, write coordinate proofs about
properties of triangles. For advanced students, include
problems in which coordinates are variables.
Use geometric shapes, their measures and their
properties to describe objects. Use units and define
quantities appropriately for the purpose of descriptive
modeling. Choose an appropriate level of accuracy.
text
reference
4-1, 4-6
5-4
4-2
G.CO.C.10
G.CO.C.10
A.REI.A.1
A.REI.B.3
various
sections
8.G.A.1
G.CO.B.7
G.CO.B.6
G.CO.B.7
G.CO.B.8
G.CO.B.8
G.CO.C.10
G.CO.C.9
G.CO.C.10
4-3
4-3
4-4, 4-5
various
sections
4-7
G.CO.C.10
G.GPE.B.4
4-7
G.MG.A.1
N.Q.A.1
N.Q.A.2
N.Q.A.3
various
sections
supplement
Optional enrichment: Write and solve inequalities to
find possible side lengths for triangles.
Vocabulary
AAS Theorem
acute triangle
altitude
ASA Theorem
base angle
corollary
equilateral/equiangular triangle
exterior angle
HL Theorem
included angle
included side
isosceles triangle
median
obtuse triangle
remote interior angles
right triangle
SAS Theorem
scalene triangle
SSS Theorem
triangle inequality
vertex angle
Additional Resources
Optional, high quality resources that support the unit.
A.CED.A.1
A.REI.B.3
5-4
supplement