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# 5-6 - PowerPoint PPT Presentation

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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Congruence

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

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°

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°

Learn to use properties of congruent figures to solve problems.

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.

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.

[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.

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.

[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: 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

[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: 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

[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

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

A. Find a.

Subtract 8 from both sides.

ML @ YX

6b = 30

6b = 30

6 6

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

B. Find b.

Divide both sides by 6.

b = 5

J @V

5c = 85

5c = 85

5 5

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

C. Find c.

Divide both sides by 5.

c = 17

IH @ RS

3a = 6

3a = 6

3 3

Try This: Example 2A

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

H @S

4b = 120

4b = 120

4 4

Try This: Example 2B

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

K @T

c + 10 = 30

c + 10 = 30

–10 –10

Try This: Example 2C

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

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

In the figure, [email protected]

10

80°

2. Find mB.

1. Find XY.

8

3. Find CD.

90°

4. Find mZ.