Transcript Applied Geometry

Geometry
Lesson 4 – 3
Congruent Triangles
Objective:
Name and use corresponding parts of congruent polygons.
Prove triangles congruent using the definition of congruence.
Congruent
Congruent

Figures that have exactly the same shape and
size
Are the following congruent?
Congruent, all same shape
and size
Not congruent, same shape,
but not the same size.
Congruent Polygons
Congruent Polygons

All parts are congruent (angles and sides)
Corresponding parts

Parts of the polygons that ‘match up’
Two polygons are congruent if and only
if their corresponding parts are
congruent.
Corresponding angles
Corresponding Sides
Congruence Statement
Have to be in matching order
Show that the polygons are congruent by
identifying all the congruent corresponding
parts. Then write a congruence statement.
Congruence Statement:
If and only if
If two polygons are congruent, then their
corresponding parts are congruent.
Corresponding parts of congruent
triangles are congruent

Abbreviation: CPCTC
CPCTC can/will be used as a reason in proofs.
NEED TO KNOW!
ABC  DFE Find the values of x and y.
Use your congruence statement
to match up parts.
8y – 5 = 99
8y = 104
y = 13
2y + x = 38.4
2(13) + x = 38.4
26 + x = 38.4
x = 12.4
RSV  TVS Find the values of x and y.
12
mR  180  90  78  12
x = 12
2y – 1 = 24
2y = 25
y = 12.5
Theorem 4.3
Third Angle Theorem

If two angles of one triangle are congruent
to two angles of a second triangle, then the
third angles of the triangle are congruent.
The planners of the Senior Banquet decide to
fold dinner napkins using the Triangle Pocket
Fold so that they can place a small gift in the
pocket.
If NPQ  RST , and mNPQ  40, find mSRT .
mRTS  mRST  90
mRTS  40  90
mRTS  50
Given : DE  GE, DF  GF ,
D  G, DFE  GFE
Pr ove : DEF  GEF
Theorem 4.4
Properties of Triangle Congruence
Reflexive
ABC  ABC
Symmetric
If ABC  EFG, then EFG  ABC .
Transitive
If ABC  EFG and EFG  JKL,
then EFG  ABC .
Homework
Pg. 256 1 – 7 all, 10 – 20 E, 24, 58