Pre-Algebra

5-6 Congruence5-6 Congruence

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

5-6 Congruence

Warm UpFind the measure of the indicated angle.

Pre-Algebra

5-6 Congruence

1. the fourth angle in a quadrilateral containing angles of 100°, 130°, and 75°

2. the third angle of a right triangle with an angle of 60°

3. the supplement of a 35° angle

55°

30°

145°

Pre-Algebra

5-6 Congruence

Problem of the DayThe measure of ABC is 14° less than the measure of its complement, CBD. What is the measure of each angle?

mABC = 38°; mCBD = 52°

Pre-Algebra

5-6 Congruence

Learn to use properties of congruent figures to solve problems.

Pre-Algebra

5-6 Congruence

correspondence

Vocabulary

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.

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.

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.

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.

|

||

|||

||||

|

||

|||

||||

Write a congruence statement for the pair of polygons.

60° 60°

120° 120°

60° 60°

120° 120°

Pre-Algebra

5-6 Congruence

Try This: Example 1B

The vertices in the first pentagon are written in order around the pentagon 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°

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

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

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

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.

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

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.

Pre-Algebra

5-6 Congruence

Explain what it means for two polygons to be congruent.

Pre-Algebra

5-6 Congruence

What’s the Error?

Explain the error in the congruence statement and write a correct congruence statement.

30˚30˚

60˚ 60˚

Triangle ABC triangle DEF

A

B

C

E

DF

Pre-Algebra

5-6 Congruence

Lesson Quiz

In the figure, WXYZ ABCD

1. Find XY. 2. Find mB.

3. Find CD. 4. Find mZ.

10 80°

8 90°