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Learn to use properties of congruent figures to solve problems. 5-6. Congruence. Pre-Algebra. 5-6. Congruence. Pre-Algebra. 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.

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Presentation Transcript
slide2
5-6

Congruence

Pre-Algebra

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.

slide3
5-6

Congruence

55

55

Pre-Algebra

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.

slide4
5-6

Congruence

Pre-Algebra

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.

slide5
–8 –8

WX ≅ KL

a + 8 = 24

5-6

Congruence

a = 16

Pre-Algebra

Example 2A: Using Congruence Relationships to Find Unknown Values

In the figure, quadrilateral VWXY≅ quadrilateral JKLM.

A. Find a.

Subtract 8 from both sides.

slide6
6b = 30

ML ≅ YX

6b = 30

5-6

Congruence

6 6

Pre-Algebra

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

slide7
5c = 85

∠J ≅∠V

5c = 85

5-6

Congruence

5 5

Pre-Algebra

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

slide8
5-6

Congruence

Pre-Algebra

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.

slide9
5-6

Congruence

Pre-Algebra

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.

slide10
5-6

Congruence

Pre-Algebra

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

slide11
3a = 6

IH ≅ RS

3a = 6

5-6

Congruence

3 3

Pre-Algebra

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

slide12
4b = 120

∠H ≅∠S

4b = 120

5-6

Congruence

4 4

Pre-Algebra

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

slide13
–10 –10

c + 10 = 30

∠K ≅∠T

c + 10 = 30

5-6

Congruence

Pre-Algebra

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

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