7-6 Congruence

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpFind the measure of the indicated angle.

Course 3

7-6 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°

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

Course 3

7-6 Congruence

mABC = 38°; mCBD = 52°

M8G1.d:

How do I use the properties of congruent figures to solve problems?

Course 3

7-6 Congruence

Course 3

7-6 Congruence

correspondence

Vocabulary

Course 3

7-6 Congruence

A correspondence is a way of matching up two sets of objects.

If 2 polygons are congruent, all of their corresponding sides and angles are congruent. In a congruence statement, the vertices (each vertex) in the 2nd polygon are written in order of correspondence with the 1st polygon.

Course 3

7-6 Congruence

Marks on the sides of a figure can be used to show congruence.

AB QR (2 marks)

BC PR (3 marks)

AC = PQ (1 mark)

Helpful Hint

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Course 3

7-6 Congruence

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 each pair of polygons.

65 65

Course 3

7-6 Congruence

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 each pair of polygons.

Course 3

7-6 Congruence

Check It Out: 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 each pair of polygons.

60° 60°

120° 120°

60° 60°

120° 120°

Course 3

7-6 Congruence

Check It Out: 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 each pair of polygons.

140° 140°

110°

110°

110°

110°

140°

140°

110°

110°

110°

110°

Course 3

7-6 Congruence

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.

Find a.

a + 8 = 24 WX KL

Course 3

7-6 Congruence

In the figure, quadrilateral VWXY quadrilateral JKLM.

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

Find b.6b = 30 ML YX

b = 5

Example 2B: Using Congruence Relationships to Find Unknown Values

Course 3

7-6 Congruence

5c = 85 J V

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

Find c.

c = 17

In the figure, quadrilateral VWXY quadrilateral JKLM.

Example 2C: Using Congruence Relationships to Find Unknown Values

Course 3

7-6 Congruence

Check It Out: Example 2A

In the figure, quadrilateral JIHK quadrilateral QRST.

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.

Course 3

7-6 Congruence

Find b.

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

b = 30°

4b = 120 H S

Check It Out: Example 2B

In the figure, quadrilateral JIHK quadrilateral QRST.

3a4b° 6

30°Q

120°R S

H I

JK c + 10°

T

Course 3

7-6 Congruence

Find c.

c = 20°

Subtract 10 from both sides.–10 –10

c + 10 = 30

c + 10 = 30 K T

Check It Out: Example 2C

3a4b° 6

30°

90°

Q

120°90° R S

H I

JK

T

c + 10°

In the figure, quadrilateral JIHK quadrilateral QRST.

Course 3

7-6 Congruence

Lesson Quiz

In the figure, WXYZ ABCD

2. Find mB.

4. Find mZ.

10 80°

8 90°

1. Find XY.

3. Find CD.