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4.1 CONGRUENT
FIGURES
Chapter 4
Congruent Triangles
Congruent Polygons
4.1 Congruent Figures
• Congruent Figures: Same size and same shape
•
-Slide, flip or turn to overlap exactly
Slide
rotate/
turn
flip
Congruent Polygons:
• All sides and angles are identical
• BUT YOU MUST NAME THEM CORRECTLY
• list corresponding vertices in the same order
• TJD = FRC
T
RCF
• this means TJ is
congruent to RC
F
C
J
D
R
Naming Congruent Parts
• Δ TJD = Δ RCF. List the corresponding parts:
Corresponding Angles:
<T =
<J =
<D =
Corresponding Sides:
TJ =
JD =
TD =
T
F
C
J
D
R
Finding Congruent Triangles
• Decide whether the triangles are congruent.
• Justify your answer.
E
3
AC ≅ EC GIVEN
4
AB≅ED AB=3=ED B
D
4
C
BC≅ DC BC=4=DC 3
<A=<E
<A ≅<E GIVEN
A
<B≅<D All right angles
are congruent
<BCA ≅ <DCE vertical angles are congruent
ΔABC ≅ΔEDC by the definition of congruent triangles
Finding Congruent Triangles
• Can you conclude that ΔJKL = ΔMNL?
J
N
Given: <J = <M and
<K = <N
L
K
M
All the angles are congruent (the same)
BUT We do not have enough information to
state that all the sides are congruent!
SO
No; Corresponding sides are not
necessarily congruent
Theorem 4-1:
• If two angles of one triangle are congruent
to two angles of another triangle, then the
third angles are congruent.
D
A
Given: <A = <D
B
C
Conclude:
<C = <F
E
F
Homework
• Pg 200-201
• TODAY : 3-13 and 16-23,
• Tomorrow: 23-28, 38-41, 44