GEOMETRY
Triangle Congruence
OBJECTIVE #: G.CO.7
OBJECTIVE
 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.
BIG IDEA (Why is this included in the curriculum?)
 If two triangles are congruent, then their corresponding angles and sides are congruent.
PREVIOUS KNOWLEDGE (What skills do they need to have to succeed?)
 The student must identify the parts, sides and angles, of a given triangle.
 The student must understand congruent segments have the same length.
 The student must understand congruent angles have the same measure.
VOCABULARY USED IN THIS OBJECTIVE (What terms will be essential to understand?)
PREVIOUS VOCABULARY (Terms used but defined earlier)
 Angle: A geometric figure formed by rotating a ray about its initial point.
 Corresponding Parts of Congruent Figures: The sides or angles that are in corresponding
positions when two figures are congruent.
 CPCFC: Corresponding Parts of Congruent Figures are Congruent.
 Side of a Polygon: The segment formed by connecting two adjacent vertices of a polygon.
 Triangle: A figure formed by three segments joining three non-collinear points, called vertices.
NEW VOCABULARY (New Terms and definitions introduced in this objective)
SKILLS (What will they be able to do after this objective?)
 Students will be able to identify corresponding angles and sides based on congruence statements.
 Students will be able to develop and write congruence statements for two congruent triangles by
identifying corresponding parts.
 Students will be able to determine if two triangles are congruent based on their corresponding parts.
SHORT NOTES (A short summary of notes so that a teacher can get the basics of what is expected.)
 The student needs to understand that the order of the congruency statement matters.
 Some figures may need to be re-drawn in to make it easier to identify corresponding parts.
 The big idea here is to move from CPCFC to CPCTC (Figures to Triangles)
 Given the following diagrams, state the congruency statement as well as the rigid motion used to map
one triangle onto the other.
Congruency Statements may vary.
C
Z
Y
Sample: ΔBAC ≅ ΔYZX
A
B
X
Translate ΔBAC along vector ⃗⃗⃗⃗⃗
𝐶𝑋 then rotate until ΔBAC maps onto ΔYZX.
MISCONCEPTIONS (What are the typical errors or difficult areas? Also suggest ways to teach them.)
 Students tend to focus on diagrams rather than congruency statements.
 Students may think the congruency statements have to be written in alphabetical order.
FUTURE CONNECTIONS (What will they use these skills for later?)
 Triangle congruency and transformations will be utilized to discover the characteristics of different
quadrilaterals.
ADDITIONAL EXTENSIONS OR EXPLANATIONS (What needs greater explanation?)
 Sequences of rigid motions will be used to discover congruence postulates for triangles.
ASSESSMENTS (Questions that get to the heart of the objective – multiple choice, short answer, multi-step)
1. Given ∆TUV ≅ ∆WXY, find the values of x and y.
x = 8 and y = 16
2. Given that ∆PQR ≅ ∆XYZ, m∠P = (7n + 5)°, m∠Q = (3n – 5)°, and m∠Z = 30°, what is the value of n?
n = 15
3. Given that ∆JKL ≅ ∆RST, JK = 3z + 21, KL = 2z + 25, LJ = 21 – 3z and ST = 5z + 31, what is the value of z?
z = -2
From CCSD Geometry Honors Semester 1 Practice Exam 2012 - 2013
1. On the coordinate plane, draw triangles ABC and ABC such that:
(1) A = A
(2) ABC has been rotated 90°.
Answers will vary. Sample is shown at the right.
2. In the diagram, m is the perpendicular bisector of AB at C, and rm  D   E .
m
E
D
A
C
B
Prove ADC  BEC .
Given m is the perpendicular bisector of ̅̅̅̅
𝐴𝐵 and D maps onto E, then A maps onto B, and C maps onto
itself. Therefore ΔADC ≅ ΔBEC.