Learn
This presentation is the property of its rightful owner.
Sponsored Links
1 / 13

Pre-Algebra PowerPoint PPT Presentation


  • 57 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

Pre-Algebra

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Pre algebra

Learn to use properties of congruent figures to solve problems.

5-6

Congruence

Pre-Algebra


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.

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

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.


Pre algebra

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.


Pre algebra

–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.


Pre algebra

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


Pre algebra

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


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.

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

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.


Pre algebra

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


Pre algebra

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


Pre algebra

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


Pre algebra

–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


  • Login