Holt CA Course 1

8-6 Congruent Polygons

MG3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationship between the sides and angles of the two figures.

California Standards

Holt CA Course 1

8-6 Congruent PolygonsA correspondence is a way of matching up two sets of objects.

Congruent figures have the same shape and size. If two polygons are congruent, all of their corresponding sides and angles are congruent.

To write a congruence statement, the vertices in the second polygon have to be written in order of correspondence with the first polygon.

Holt CA Course 1

8-6 Congruent Polygons

Additional Example 1: Writing Congruent Statements

A corresponds to Q. A Q

B corresponds to R. B R

C corresponds to P. C P

The congruence statement is triangle ABC triangle QRP.

A. Write a congruence statement for each pair of polygons.

55 55

Holt CA Course 1

8-6 Congruent PolygonsAdditional Example 1: Writing Congruent Statements

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

D corresponds to M. D M

E corresponds to N. E N

F corresponds to O. F O

The congruence statement is pentagon DEFGH pentagon MNOPQ.

G corresponds to P. G P

H corresponds to Q. H Q

B. Write a congruence statement for each pair of polygons.

Holt CA Course 1

8-6 Congruent PolygonsCheck It Out! Example 1

A corresponds to S. A S

B corresponds to T. B T

C corresponds to Q. C Q

The congruence statement is trapezoid ABCD trapezoid STQR.

A B

CD

Q R

ST

D corresponds to R. D R

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A. Write a congruence statement for each pair of polygons.

60° 60°

120° 120°

60° 60°

120° 120°

Holt CA Course 1

8-6 Congruent PolygonsCheck It Out! Example 1

A corresponds to M. A M

B corresponds to N. B N

C corresponds to O. C O

The congruence statement is hexagon ABCDEF hexagon MNOPQL.

D corresponds to P. D P

E corresponds to Q. E Q

A B

C

DE

F

N

O

P

QL

MF corresponds to L. F L

B. Write a congruence statement for each pair of polygons.

140° 140°

110°

110°

110°

110°

140°

140°

110°

110°

110°

110°

Holt CA Course 1

8-6 Congruent PolygonsAdditional Example 2: Using Congruence Relationships to

Find Unknown ValuesIn the figure, quadrilateral VWXY quadrilateral JKLM.

a = 16

–8 –8 Subtract 8 from both sides.

A. Find a.

a + 8 = 24 WX KL

Holt CA Course 1

8-6 Congruent Polygons

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 2: Using Congruence Relationships to Find Unknown Values

Holt CA Course 1

8-6 Congruent Polygons

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 2: Using Congruence Relationships to Find Unknown Values

Holt CA Course 1

8-6 Congruent PolygonsCheck It Out! Example 2

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.

Holt CA Course 1

8-6 Congruent Polygons

B. Find b.

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

b = 30

4b = 120 H S

Check It Out! Example 2

In the figure, quadrilateral JIHK quadrilateral QRST.

3a4b° 6

30°Q

120°R S

H I

JK c + 10°

T

Holt CA Course 1

8-6 Congruent Polygons

C. Find c.

c = 20

Subtract 10 from both sides.–10 –10

c + 10 = 30

c + 10 = 30 K T

Check It Out! Example 2

3a4b° 6

30°

90°

Q

120°90° R S

H I

JK

T

c + 10°

In the figure, quadrilateral JIHK quadrilateral QRST.