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Congruent Figures
Academic Geometry
Congruent Figures
Congruent figures have the same size and shape.
When two figures are congruent, you can move
one so that it fits exactly on the other one.
Congruent Figures
Three ways to make such a move – a slide, a flip,
a turn
Flip
slide
turn
Congruent Figures
Congruent polygons have congruent
corresponding parts – their matching sides
and angles.
Matching vertices are corresponding vertices.
When you name congruent polygons, always
list corresponding vertices in the same order.
Congruent Figures
b
q
y
x
a
c
r
p
Is this a flip a slide or a turn? ____________
What corresponds to angle C? __________
What corresponds to angle B? __________
AX corresponds to __________________
Naming Congruent Parts
d
j
t
f
r
Triangle TJD is congruent to Triangle RCF.
List the congruent corresponding parts.
Sides: ___________ ____________ __________
Angles: _________ __________ __________
Naming Congruent Parts
Triangle WYS is congruent to triangle MKV.
List the congruent corresponding parts.
Use three letters to name each angle.
drawing
Sides:
Angles:
Finding Congruent Triangles
Two triangles are congruent when they have
three pairs of congruent corresponding sides
and three pairs of congruent corresponding
angles.
Finding Congruent Triangles
Decide whether the triangles are congruent.
Justify your answer.
Justify
3
4
b
Congruent
e
c
3
a
4
d
Finding Congruent Triangles
Decide whether the triangles are congruent.
Justify your answer.
n
j
l
k
Congruent
m
Justify
Theorem 4-1
If two angles of one triangle are congruent to
two angles of another triangle, then the third
angles are congruent.
a
b
d
c
e
Angle C is congruent to Angle F
f
Proving Triangles Congruent
Given PQ congruent PS, QR congruent SR,
<Q congruent <S, <QPR congruent SPR
Prove Triangle PQR congruent PSR
p
s
q
Statement
Reason
r
Proving Triangles Congurent
Given: < A congruent <D, <E congruent <C, AE congruent DC,
EB congruent CB, BA congruent BD
Prove: Triangle AEB congruent DCB
b
a
Statement
c
Reason
d
e