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Transcript
Congruent Figures
Lesson 4-1
Geometry
Additional Examples
ABC
QTJ. List the congruent corresponding
parts.
List the corresponding vertices in the same order.
Angles: A @ Q
B @ T
C @ J
List the corresponding sides in the same order.
Sides: AB @ QT
BC @ TJ
AC @ QJ
Congruent Figures
Lesson 4-1
Geometry
Additional Examples
XYZ
KLM, mY = 67, and mM = 48. Find mX.
Use the Triangle Angle-Sum Theorem and the definition of congruent
polygons to find mX.
mX + mY + mZ = 180
Triangle Angle-Sum Theorem
mZ = mM
Corresponding angles of congruent
triangles that are congruent
mZ = 48
Substitute 48 for mM.
mX + 67 + 48 = 180
mX + 115 = 180
mX = 65
Substitute.
Simplify.
Subtract 115 from each side.
Congruent Figures
Lesson 4-1
Geometry
Additional Examples
Can you conclude that
ABC
CDE in the figure below?
List corresponding vertices in the same order.
If
ABC
CDE, then BAC
DCE.
The diagram above shows BAC
DEC, not DCE.
Corresponding angles are not necessarily congruent, therefore you
cannot conclude that ABC
CDE.
Congruent Figures
Lesson 4-1
Additional Examples
Geometry
Show how you can conclude that CNG
DNG. List
statements and reasons.
Congruent triangles have three congruent corresponding
sides and three congruent corresponding angles.
Examine the diagram, and list the congruent corresponding
parts for CNG and DNG.
a. CG DG
b. CN DN
c. GN GN
d. C D
e. CNG DNG
f. CGN DGN
g. CNG
DNG
Given
Given
Reflexive Property of Congruence
Given
Right angles are congruent.
If two angles of one triangle are congruent to two angles
of another triangle, then the third angles are congruent.
(Theorem 4-1.)
Definition of triangles