Warm Up 1. How many sides does a hexagon have? 2. How many sides does a pentagon have? 3. How many angles does an octagon have? 4. Evaluate ( n – 2)180 for n = 7. 6. 5. 8. 900. Find the measure of the indicated angle.
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Warm Up
1. How many sides does a hexagon have?
2. How many sides does a pentagon have?
3. How many angles does an octagon have?
4. Evaluate (n – 2)180 for n = 7.
6
5
8
900
Find the measure of the indicated angle.
5. the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75°
55°
6. the third angle of a right triangle with an angle of 60°
30°
7. the supplement of a 35° angle
145°
Congruency
Polygons
A polygon is a closed plane figure formed by three or more segments. A polygon is named by the number of its sides.
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
ngon
n
Polygon
Number of Sides
Learn to use properties of congruent figures to solve problems.
Vocabulary
correspondence
A correspondence is a way of matching up two sets of objects.
If two polygons are congruent, all of their corresponding sides and angles are congruent. In a congruence statement, the vertices in the second polygon are written in order of correspondence with the first polygon.
Helpful Hint
Marks on the sides of a figure can be used to show congruence.
[email protected] (1 mark)
[email protected] (2 mark)
[email protected] (3 mark)
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__
__
__
__
__
55
55
Writing Congruent Statements
Write a congruence statement for each pair of polygons.
The first triangle can be named triangle ABC. To complete the congruence statement, the vertices in the second triangle have to be written in order of the correspondence.
A@Q, so A corresponds to Q.
B@R, so B corresponds to R.
C@P, so C corresponds to P.
The congruence statement is triangle ABC@ triangle QRP.
Writing Congruent Statements
Write a congruence statement for each pair of polygons.
The vertices in the first pentagon are written in order around the pentagon starting at any vertex.
D@M, so D corresponds to M.
E@N, so E corresponds to N.
F@O, so F corresponds to O.
G@P, so G corresponds to P.
H@Q, so H corresponds to Q.
The congruence statement is pentagon DEFGH@ pentagon MNOPQ.
Try this!
Write a congruence statement for each pair of polygons.
The first trapezoid can be named trapezoid ABCD. To complete the congruence statement, the vertices in the second trapezoid have to be written in order of the correspondence.
A
B

60°
60°


120°
120°

D
C
A@S, so A corresponds to S.
Q
R

120°
120°
B@T, so B corresponds to T.


C@Q, so C corresponds to Q.
60°
60°

D@R, so D corresponds to R.
T
S
The congruence statement is trapezoid ABCD@ trapezoid STQR.
Try this!
Write a congruence statement for each pair of polygons.
The vertices in the first pentagon are written in order around the pentagon starting at any vertex.
110°
A
B
A@M, so A corresponds to M.
110°
140°
140°
F
B@N, so B corresponds to N.
C
110°
C@O, so C corresponds to O.
E
110°
D
N
D@P, so D corresponds to P.
110°
O
M
E@Q, so E corresponds to Q.
140°
110°
110°
F@L, so F corresponds to L.
P
140°
L
The congruence statement is hexagon ABCDEF@ hexagon MNOPQL.
110°
Q
WX @ KL
a + 8 = 24
–8 –8
a = 16
Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral VWXY@ quadrilateral JKLM.
Find a.
Subtract 8 from both sides.
ML @ YX
6b = 30
6b = 30
6 6
Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral VWXY@ quadrilateral JKLM.
Find b.
Divide both sides by 6.
b = 5
J @V
5c = 85
5c = 85
5 5
Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral VWXY@ quadrilateral JKLM.
Find c.
Divide both sides by 5.
c = 17
IH @ RS
3a = 6
3a = 6
3 3
Try This!
In the figure, quadrilateral JIHK@ quadrilateral QRST.
Find a.
Divide both sides by 3.
3a
I
H
a = 2
6
4b°
S
R
120°
J
30°
Q
c + 10°
K
T
H @S
4b = 120
4b = 120
4 4
Try This!
In the figure, quadrilateral JIHK@ quadrilateral QRST.
Find b.
Divide both sides by 4.
3a
I
H
b = 30°
6
4b°
S
R
120°
J
30°
Q
K
c + 10°
T
K @T
c + 10 = 30
c + 10 = 30
–10 –10
Try This!
In the figure, quadrilateral JIHK@ quadrilateral QRST.
Find c.
Subtract 10 from both sides.
3a
I
H
6
S
c = 20°
R
90°
4b°
90°
120°
30°
J
Q
c + 10°
K
T
Congruence
Congruence Statements
Finding Unknown Values