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5-6. Congruence. Warm Up. Problem of the Day. Lesson Presentation. Pre-Algebra. Learning Goal Assignment Learn to use properties of congruent figures to solve problems. Vocabulary. correspondence. A correspondence is a way of matching up two sets of objects. - PowerPoint PPT Presentation
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Page 1: 5-6
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Pre-Algebra

5-6 Congruence5-6 Congruence

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

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Pre-Algebra

5-6 Congruence

Learning Goal Assignment

Learn to use properties of congruent figures to solve problems.

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Pre-Algebra

5-6 Congruence

correspondence

Vocabulary

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Pre-Algebra

5-6 Congruence

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.

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Pre-Algebra

5-6 Congruence

Additional Example 1A: Writing Congruent Statements

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.

Write a congruence statement for the pair of polygons.

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Pre-Algebra

5-6 Congruence

Try This: Example 1A

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 S, so A corresponds to S.

B T, so B corresponds to T.

C Q, so C corresponds to Q.

The congruence statement is trapezoid ABCD trapezoid STQR.

A B

CD

Q R

STD R, so D corresponds to R.

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Write a congruence statement for the pair of polygons.

60° 60°

120° 120°

60° 60°

120° 120°

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Pre-Algebra

5-6 Congruence

Pre-Algebra HW

Page 741

#1-10

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Pre-Algebra

5-6 Congruence

Additional Example 1B: Writing Congruent Statements

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.

The congruence statement is pentagon DEFGH pentagon MNOPQ.

G P, so G corresponds to P.

H Q, so H corresponds to Q.

Write a congruence statement for the pair of polygons.

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Pre-Algebra

5-6 Congruence

Try This: Example 1B

The vertices in the first hexagon are written in order around the hexagon starting at any vertex.

A M, so A corresponds to M.

B N, so B corresponds to N.

C O, so C corresponds to O.

The congruence statement is hexagon ABCDEF hexagon MNOPQL.

D P, so D corresponds to P.

E Q, so E corresponds to Q.

A B

C

DE

F

N

O

P

QL

M

F L, so F corresponds to L.

Write a congruence statement for the pair of polygons.

140° 140°

110°

110°

110°

110°

140°

140°

110°

110°

110°

110°

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Pre-Algebra

5-6 Congruence

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

In the figure, quadrilateral VWXY quadrilateral JKLM.

a = 16

–8 –8 Subtract 8 from both sides.

A. Find a.

a + 8 = 24 WX KL

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Pre-Algebra

5-6 Congruence

Try This: Example 2A

In the figure, quadrilateral JIHK quadrilateral QRST.

A. Find a.

3a4b° 6

30°Q

120°R S

H I

JK

3a = 6 3 3

a = 2

c + 10°T

3a = 6 IH RS

Divide both sides by 3.

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Pre-Algebra

5-6 Congruence

In the figure, quadrilateral VWXY quadrilateral JKLM.

6 6 6b = 30 Divide both sides by 6.

B. Find b.6b = 30 ML YX

b = 5

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

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Pre-Algebra

5-6 Congruence

B. Find b.

Divide both sides by 4. 4 4 4b = 120

b = 30°

4b = 120 H S

Try This: Example 2B

In the figure, quadrilateral JIHK quadrilateral QRST.

3a4b° 6

30°Q

120°R S

H I

JK c + 10°

T

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Pre-Algebra

5-6 Congruence

5c = 85 J V

5 5 5c = 85 Divide both sides by 5.

C. Find c.

c = 17

In the figure, quadrilateral VWXY quadrilateral JKLM.

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

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Pre-Algebra

5-6 Congruence

C. Find c.

c = 20°

Subtract 10 from both sides.–10 –10

c + 10 = 30

c + 10 = 30 K T

Try This: Example 2C

3a4b° 6

30°

90°

Q

120°90° R S

H I

JK

T

c + 10°

In the figure, quadrilateral JIHK quadrilateral QRST.

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Pre-Algebra

5-6 Congruence5-7 Transformations

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

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5-7Learning Goal Assignment

Learn to transform plane figures using translations, rotations, and reflections.

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Vocabulary

transformation

translation

rotation

center of rotation

reflection

image

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When you are on an amusement park ride,you are undergoing a transformation. Ferris wheels and merry-go-rounds are rotations. Free fall rides and water slides are translations. Translations, rotations, and reflections are type of transformations.

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The resulting figure or image, of a translation, rotation or reflection is congruent to the original figure.

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Additional Example 1A & 1B: Identifying Transformations

Identify each as a translation, rotation, reflection, or none of these.

A. B.

reflection rotation

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Try This: Example 1A & 1B

Identify each as a translation, rotation, reflection, or none of these.

A

B C

A. B. A B

CD

A’ B’

C’D’

translation reflection

A’

B’ C’

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Additional Example 1C & 1D: Identifying Transformations

Identify each as a translation, rotation, reflection, or none of these.

C. D.

none of the these translation

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Identify each as a translation, rotation, reflection, or none of these.

BC

DE

F

C. D.

A

A’

B’C’

D’

F’

E’

rotation none of these

Try This: Example 1C & 1D

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Additional Example 2A: Drawing Transformations

Draw the image of the triangle after the transformation.

A

B

C

A. Translation along AB so that A’ coincides with B

A’

B’

C’

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Try This: Example 2A

Draw the image of the polygon after the transformation.

A

B C

D

E

F

A’

B’ C’

D’

E’

F’

A. Translation along DE so that E’ coincides with D

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Additional Example 2B: Drawing Transformations

Draw the image of the triangle after the transformation.

A

B

C

B. Reflection across BC.

A’

B’

C’

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Try This: Example 2B

Draw the image of the polygon after the transformation.

A

BC

D

E

F

B. Reflection across CD.

A’

B’C’

D’

E’

F’

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Draw the image of the triangle after the transformation.

A

B

C

C. 90° clockwise rotation around point B A’

B’

C’

Additional Example 2C: Drawing Transformations

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Draw the image of the polygon after the transformation.

A

BC

D

E

F

C’

A’

B’

D’

E’F’

C. 90° counterclockwise rotation around point C

Try This: Example 2C

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Additional Example 3A: Graphing Transformations

Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation.

A. 180° counterclockwise rotation around (0, 0)

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Try This: Example 3A

Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation.

A. 180° clockwise rotation around (0, 0)

x

y

–2

2

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Additional Example 3B: Graphing Transformations

Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation.

B. Translation 5 units left

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B. Translation 10 units left

Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation.

Try This: Example 3B

x

y

–2

2

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Additional Example 3C: Graphing Transformations

Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation.

C. Reflection across the x-axis

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C. Reflection across the x-axis

Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation.

Try This: Example 3C

x

y

–2

2


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