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5-6. Congruence. Warm Up. Problem of the Day. Lesson Presentation. Pre-Algebra. 5-6. Congruence. Pre-Algebra. Warm Up Find the measure of the indicated angle. 1 . the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75°. 55°.

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5 6

5-6

Congruence

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra


5 6

5-6

Congruence

Pre-Algebra

Warm Up

Find the measure of the indicated angle.

1. the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75°

55°

2. the third angle of a right triangle with an angle of 60°

30°

3. the supplement of a 35° angle

145°


5 6

Problem of the Day

The measure of ABC is 14° less than the measure of its complement, CBD. What is the measure of each angle?

mABC = 38°; mCBD = 52°


5 6

Learn to use properties of congruent figures to solve problems.


5 6

Vocabulary

correspondence


5 6

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.


5 6

Additional Example 1A: Writing Congruent Statements

Write a congruence statement for the 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.


5 6

Additional Example 1B: Writing Congruent Statements

Write a congruence statement for the 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.


5 6

Try This: Example 1A

Write a congruence statement for the 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.


5 6

Try This: Example 1B

Write a congruence statement for the 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


5 6

WX @ KL

a + 8 = 24

–8 –8

a = 16

Additional Example 2A: Using Congruence Relationships to Find Unknown Values

In the figure, quadrilateral VWXY@ quadrilateral JKLM.

A. Find a.

Subtract 8 from both sides.


5 6

ML @ YX

6b = 30

6b = 30

6 6

Additional Example 2B: Using Congruence Relationships to Find Unknown Values

In the figure, quadrilateral VWXY@ quadrilateral JKLM.

B. Find b.

Divide both sides by 6.

b = 5


5 6

J @V

5c = 85

5c = 85

5 5

Additional Example 2C: Using Congruence Relationships to Find Unknown Values

In the figure, quadrilateral VWXY@ quadrilateral JKLM.

C. Find c.

Divide both sides by 5.

c = 17


5 6

IH @ RS

3a = 6

3a = 6

3 3

Try This: Example 2A

In the figure, quadrilateral JIHK@ quadrilateral QRST.

A. Find a.

Divide both sides by 3.

3a

I

H

a = 2

6

4b°

S

R

120°

J

30°

Q

K

c + 10°

T


5 6

H @S

4b = 120

4b = 120

4 4

Try This: Example 2B

In the figure, quadrilateral JIHK@ quadrilateral QRST.

B. Find b.

Divide both sides by 4.

3a

I

H

b = 30°

6

4b°

S

R

120°

J

30°

Q

K

c + 10°

T


5 6

K @T

c + 10 = 30

c + 10 = 30

–10 –10

Try This: Example 2C

In the figure, quadrilateral JIHK@ quadrilateral QRST.

C. Find c.

Subtract 10 from both sides.

3a

I

H

c = 20°

6

90°

4b°

S

R

120°

90°

J

30°

c + 10°

Q

K

T


5 6

Explain what it means for two polygons to be congruent.


5 6

What’s the Error?

Explain the error in the congruence statement and write a correct congruence statement.

B

E

60˚

60˚

30˚

30˚

F

A

D

C

Triangle ABC triangle DEF


5 6

Lesson Quiz

In the figure, [email protected]

10

80°

2. Find mB.

1. Find XY.

8

3. Find CD.

90°

4. Find mZ.


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