Chapter 4 – Congruent
Triangles
4-1 Congruent Figures
4-1 Congruent Figures
(DNG pages 72-74,
text reference pages 198-200)
Objective: Recognize congruent figures and their corresponding parts.
Vocabulary
Congruent polygons are figures that have the same size and shape.
Congruent polygons have congruent corresponding parts
Matching sides are corresponding sides.
Matching angles are corresponding angles.
Matching vertices are corresponding vertices.
When you name congruent polygons,
always list corresponding vertices
in the same order.
DEF ≅ GHI
When two figures are congruent,
you can move one so that it fits exactly on the other one.
Examples
T
C
QJ
BC
180
m M
48
67
48
115
65
Examples
DCE
DEC
is not
DC
CDE
DE
DEC
EC
ACB
ABC
EDC
WYS  MKV
35
YSW  K VM
SWY
 VMK
No, corresponding sides are not congruent.
Practice 4-1
(DNG page 317)
Congruent Figures
Each pair of polygons is congruent. Find the measures of the numbered angles.
m1 = 110, m2 = 120
m3 = 90, m4 = 135
m5 = 140, m6 = 90,
m7 = 40, m8 = 90
CAT ≅ JSD. List each of the following.
4. three pairs of congruent sides
5. three pairs of congruent angles
C ≅ J , A≅ S , T ≅ D
Practice 4-1
WXYZ ≅ JKLM.
Congruent Figures
(DNG page 317)
List each of the following.
////
6. four pairs of congruent sides
/

//
7. four pairs of congruent angles
W ≅ X
X ≅ K
Y ≅ L
//
Z ≅ M
State whether the pairs of figures are congruent. Explain.
YES
X


 GHJ ≅ IHJ
by Theorem 4-1
 HJ ≅ HJ
by Reflexive Prop. of ≅,
NO
 RSQ ≅ VST
by Vertical s Theorem
 QRS ≅ TSV
by Theorem 4-1
but none of the
sides are
necessarily ≅.
GHJ ≅ IHJ
by the definition of ≅ triangles.

Practice 4-1
Congruent Figures
(DNG page 317)
10. Developing Proof
Use the information given in the diagram.
Give a reason that each statement is true.
 Given
 Vertical Angles Theorem
 Theorem 4-1
 Given
 Definition of ≅ Triangles