Download LESSON 4-1: CONGRUENT FIGURES/POLYGONS

LESSON 4-1: CONGRUENT FIGURES/POLYGONS
Examples of Polygons
Not Polygons
POLYGON: A polygon is a closed plane figure formed by three or more segments. Each
segment intersects exactly two other segments, but only at their endpoints, and no two segments
with a common endpoint are collinear. The vertices of the polygon are the endpoints of the
sides. When naming a polygon, start with any vertex and list the points in order, either
clockwise or counter clockwise.
Congruent polygons have congruent corresponding parts—their matching sides and angles.
When you name congruent polygons, you must list corresponding vertices in the same order.
D
EXAMPLE:
C
E
F
ABCDEFGH
A
B
H
G
* Use the figures above to complete each congruence statement.
AB 
BC 
CD 
DA 
<A 
<B 
<C 
<D 
PRACTICE:
∆WYS  ∆MKV. State the corresponding parts using congruence statements.
Angles:
Sides:
B
EXAMPLE/PRACTICE:
E
∆ABC  ∆DEF
1) In the diagram to the right:
a) mark angles that are congruent
b) mark sides that are congruent
A
C
D
2) If m<A = 54 and m<F = 62, find the following:
m<B =
m<C =
m<D =
m<E =
F
In the previous example/practice problem, you utilized the following theorem (Third Angles
Theorem) to find the measures of angles B and E.
Third Angles Theorem (Theorem 4-1): If two angles of one triangle are congruent to two
angles of another triangle, then the third angles are congruent.
A
D
If <A  <D and <B  <E,
then <C  <F.
B
C
Examples:
F
Use ∆ABC and ∆DEF above. Complete each statement.
1) If m<A = 74, then m<D =
.
2) If m<B = 44, then m<E =
.
3) If m<C =
Examples/Practice:
1)
E
, then m<F =
.
1) Are the two triangles congruent? 2-3) Find the value of x.
2)
3)
4-5: ABCD  FGHJ. Find the measures of the given angles or lengths of the given sides.
4) mC = 5z + 20, mH = 6z + 10
5) AD = 5b + 4; FJ = 3b + 8