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5-6. Congruence. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 5-6. Congruence. Course 3. Warm Up Find the measure of the indicated angle. 1 . the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75°. 55°.

5-6

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5-6

Congruence

Warm Up

Problem of the Day

Lesson Presentation

Course 3

5-6

Congruence

Course 3

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

Congruence

Course 3

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

Congruence

Course 3

Learn to use properties of congruent figures to solve problems.

5-6

Congruence

Course 3

Vocabulary

correspondence

5-6

Congruence

Course 3

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

Congruence

55

55

Course 3

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

Congruence

Course 3

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

Congruence

Course 3

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

Congruence

Course 3

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

Congruence

WX @ KL

a + 8 = 24

–8 –8

a = 16

Course 3

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

A. Find a.

Subtract 8 from both sides.

5-6

Congruence

ML @ YX

6b = 30

6b = 30

6 6

Course 3

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

B. Find b.

Divide both sides by 6.

b = 5

5-6

Congruence

J @V

5c = 85

5c = 85

5 5

Course 3

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

C. Find c.

Divide both sides by 5.

c = 17

5-6

Congruence

IH @ RS

3a = 6

3a = 6

3 3

Course 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

5-6

Congruence

H @S

4b = 120

4b = 120

4 4

Course 3

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

5-6

Congruence

K @T

c + 10 = 30

c + 10 = 30

–10 –10

Course 3

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

5-6

Congruence

1. Find XY.

3. Find CD.

Course 3

Lesson Quiz

In the figure, [email protected]

10

80°

2. Find mB.

8

90°

4. Find mZ.