Applied Geometry
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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
mR 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 mNPQ 40, find mSRT .
mRTS mRST 90
mRTS 40 90
mRTS 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