Congruent Figures
GEOMETRY LESSON 4-1
(For help, go to Algebra Review, page 30.)
Solve each equation.
1. x + 6 = 25
2. x + 7 + 13 = 33
x = 19
x = 13
3. 5x = 540
4. x + 10 = 2x
x = 108
x = 10
5. For the triangle at the right, use the Triangle
Angle-Sum Theorem to find the value of y.
y = 50
Check Skills You’ll Need
4-1
Congruent Figures
GEOMETRY LESSON 4-1
Geometric figures are congruent if they are
the same size and shape. Corresponding
angles and corresponding sides are in the
same position in polygons with an equal
number of sides.
Two polygons are congruent polygons if
and only if their corresponding sides and
corresponding angles are congruent.
4-1
Congruent Figures
GEOMETRY LESSON 4-1
In a congruence statement, the order
of the vertices indicates the
corresponding parts.
Helpful Hint
When you write a statement such as
ABC  DEF, you are also stating
which parts are congruent.
4-1
Congruent Figures
GEOMETRY LESSON 4-1
Naming Congruent Parts
ABC
QTJ. List the congruent corresponding
parts.
List the corresponding vertices in the same order.
Angles: A
Q
B
T
C
J
List the corresponding sides in the same order.
Sides: AB
QT
BC
TJ
AC
QJ
Quick Check
4-1
Congruent Figures
GEOMETRY LESSON 4-1
Using Congruent Polygons
XYZ
KLM, mY = 67, and mM = 48. Find mX.
Use the Triangle Angle-Sum Theorem and the definition of congruent
polygons to find mX.
mX + mY + mZ = 180
Triangle Angle-Sum Theorem
mZ = mM
Corresponding angles of congruent
triangles that are congruent
mZ = 48
Substitute 48 for mM.
mX + 67 + 48 = 180
mX + 115 = 180
mX = 65
Substitute.
Simplify.
Subtract 115 from each side.
Quick Check
4-1
Congruent Figures
GEOMETRY LESSON 4-1
Finding Congruent Triangles
Can you conclude that
ABC
CDE in the figure below?
List corresponding vertices in the same order.
If
ABC
CDE, then BAC
DCE.
The diagram above shows BAC
DEC, not DCE.
Corresponding angles are not necessarily congruent, therefore you
cannot conclude that ABC
CDE.
Quick Check
4-1
Congruent Figures
GEOMETRY LESSON 4-1
Theorem 4-1
4-1
Congruent Figures
GEOMETRY LESSON 4-1
Proving Triangles Congruent
Show how you can conclude that CNG
DNG. List
statements and reasons.
Congruent triangles have three congruent corresponding
sides and three congruent corresponding angles.
Examine the diagram, and list the congruent corresponding
parts for CNG and DNG.
a. CG DG
b. CN DN
c. GN GN
d. C D
e. CNG DNG
f. CGN DGN
g. CNG
DNG
Given
Given
Reflexive Property of Congruence
Given
Right angles are congruent.
Third Angles Theorem
Definition of  triangles
Quick Check
4-1
Congruent Figures
GEOMETRY LESSON 4-1
In Exercises 1 and 2, quadrilateral WASH quadrilateral NOTE.
1. List the congruent corresponding parts.
WA NO, AS OT, SH TE, WH NE;
E
W N, A O, S T, H
2. mO = mT = 90 and mH = 36. Find mN.
144
3. Write a statement of triangle congruence.
Sample:
DFH
ZPR
4. Write a statement of triangle congruence.
Sample:
ABD
CDB
5. Explain your reasoning in Exercise 4 above.
Sample: Two pairs of corresponding sides and two
pairs of corresponding angles are given. C A
because all right angles are congruent. BD BD by the
Reflexive Property of . ABD
CDB by the
definition of congruent triangles.
4-1