Introduction into Corresponding parts of congruent figures.

1. Chapter 4Chapter 4
Congruent TrianglesCongruent Triangles
Sec. 4 – 1Sec. 4 – 1
Congruent FiguresCongruent Figures
Objective:
1) To recognize ≅ figures & their
corresponding parts

2. Identifying congruent figuresIdentifying congruent figures
 Two geometric figures are congruent ifTwo geometric figures are congruent if
they have exactly the same size andthey have exactly the same size and
shape.shape.
CONGRUENT
NOT CONGRUENT

3. Congruent PolygonsCongruent Polygons
 Are the same size and the same shape.Are the same size and the same shape.
Fit exactly on top of each otherFit exactly on top of each other
 HaveHave ≅≅ corresponding parts:corresponding parts:
Matching sides andMatching sides and ∠∠ss

4. You can make 3 kinds of moves so
that one congruent figure can fit
exactly on top of top of another

5. You can make 3 kinds of moves so
that one congruent figure can fit
exactly on top of top of another
These are called translations and are covered in chapter 9

6. You can make 3 kinds of moves so
that one congruent figure can fit
exactly on top of top of another

9. ΔΔQXTQXT ≅≅ ΔΔPHDPHD
QXQX ≅≅ PHPH

10. Naming PolygonsNaming Polygons
 Order Matters!!Order Matters!!
A
B C
DE S
TU
W
R
ABCDE ≅ WUTSR
AB ≅
ED ≅
∠B ≅
∠D ≅
∠A ≅
WU
RS
∠U
∠S
∠W

11. Ex. 1 Naming congruent partsEx. 1 Naming congruent parts
 The congruentThe congruent
triangles. Write atriangles. Write a
congruencecongruence
statement. Identify allstatement. Identify all
parts of congruentparts of congruent
corresponding parts.corresponding parts.
E
F
D
R
T
S

12. Ex. 1 Naming congruent partsEx. 1 Naming congruent parts
 The diagram indicatesThe diagram indicates
thatthat ∆DEF∆DEF ≅ ∆RST.≅ ∆RST.
The congruent anglesThe congruent angles
and sides are asand sides are as
follows:follows:
 Angles:Angles: ∠∠D≅D≅ ∠∠R,R, ∠∠EE
≅≅ ∠∠S,S, ∠∠F ≅F ≅∠∠TT
 Sides DE ≅ RS, EF ≅Sides DE ≅ RS, EF ≅
ST, FD ≅ TRST, FD ≅ TR
E
F
D
R
T
S

13. Example:Example: ΔΔWYSWYS ≅≅ ΔΔMKVMKV
 mm∠∠W = 25W = 25
 mm∠∠Y = 55Y = 55
 Find mFind m∠∠VV
W
Y
S
M
K
V
25
55
100

14. Example 2: Congruence StatementExample 2: Congruence Statement
Finish the following congruence statement:
ΔJKL ≅ Δ_ _ _
K
J
L
M
N
ΔJKL ≅ ΔNML