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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.

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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

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

n-gon

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)

__

__

__

__

__

__


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.

[email protected]Q, so A corresponds to Q.

[email protected]R, so B corresponds to R.

[email protected]P, so C corresponds to P.

The congruence statement is triangle [email protected] 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.

[email protected]M, so D corresponds to M.

[email protected]N, so E corresponds to N.

[email protected]O, so F corresponds to O.

[email protected]P, so G corresponds to P.

[email protected]Q, so H corresponds to Q.

The congruence statement is pentagon [email protected] 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

[email protected]S, so A corresponds to S.

Q

R

|||

120°

120°

[email protected]T, so B corresponds to T.

||

||||

[email protected]Q, so C corresponds to Q.

60°

60°

|

[email protected]R, so D corresponds to R.

T

S

The congruence statement is trapezoid [email protected] 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

[email protected]M, so A corresponds to M.

110°

140°

140°

F

[email protected]N, so B corresponds to N.

C

110°

[email protected]O, so C corresponds to O.

E

110°

D

N

[email protected]P, so D corresponds to P.

110°

O

M

[email protected]Q, so E corresponds to Q.

140°

110°

110°

[email protected]L, so F corresponds to L.

P

140°

L

The congruence statement is hexagon [email protected] hexagon MNOPQL.

110°

Q


WX @ KL

a + 8 = 24

–8 –8

a = 16

Using Congruence Relationships to Find Unknown Values

In the figure, quadrilateral [email protected] 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 [email protected] 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 [email protected] 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 [email protected] 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 [email protected] 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 [email protected] 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

Congruence Statements

Finding Unknown Values


Writing congruence statements
Writing Congruence Statements

  • In congruence statements, the vertices in the second polygon have to be written in order of correspondence with the first polygon. (A correspondence is a way of matching up to sets of objects).

  • If two polygons are congruent, all of their corresponding sides and angles are congruent.


Writing congruence statements1
Writing Congruence Statements

  • Quadrilateral EFGH Quadrilateral MNKL


Finding unknown values
Finding Unknown Values

  • In the figure, quadrilateral RSTU quadrilateral HIFG.

  • To find the value of g, b, & a we must create and solve an equation.


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