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Warm Up 1. How many sides does a hexagon have? 2. How many sides does a pentagon have? PowerPoint PPT Presentation


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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?

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Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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.


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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)

__

__

__

__

__

__


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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.


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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.


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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.


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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.


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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


Warm up 1 how many sides does a hexagon have 2 how many sides does a pentagon have

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

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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