1-5-15 Unit 7 Congruency and Similarity

1

Congruent Figures and

Triangles

First, we need to First, we need to look at some things.look at some things.

What makes two figures congruent?

All the corresponding sides are congruent.

All the corresponding angles are congruent.

How many ways can you name pentagon DCBAE?

A

D

C

B

E

10

Do it.

DCBAE

CBAED

BAEDC

AEDCB

EDCBA

Pick a vertex and go clockwise Pick a vertex and go counterclockwise

DEABC

CDEAB

BCDEA

ABCDE

EABCD

Name corresponding parts

Name all the angles that correspond:

A

D

C

B

E

P

I

J

K

H

D corresponds to I C corresponds to J B corresponds to K A corresponds to P E corresponds to H DCBAE IJKPH

• Name all the segments that correspond:DC corresponds to IJCB corresponds to JKBA corresponds to KPAE corresponds to PHED corresponds to HI

How many corresponding

angles are there?

How many corresponding

sides are there?

5 5

Naming & Comparing Polygons

♥ List vertices in order, either clockwise or counterclockwise.

♥ When comparing 2 polygons, begin at corresponding vertices; name the vertices in order and; go in the same direction.

♥ By doing this you can identify corresponding parts.

A

D

C

B

E

DCBAE

P

I

J

K

H

IJKPHD corresponds to I

AE corresponds to PH

Polygon Congruence Rule

If each pair of corresponding angles is congruent, and each pair of corresponding sides is congruent, then the two polygons are congruent.

What makes two figures congruent? All the corresponding

sides are congruent. All the corresponding angles are congruent.

Congruence Statements Given: These polygons are

congruent.

Remember, if they are congruent, they are EXACTLY the same.

That means that all of the corresponding angles are congruent and all of the corresponding sides are congruent.

DO NOT say that ‘all the sides are congruent” and “all the angles are congruent”, unless it is given or marked.NOT because it “LOOKS like it.

G

H

FEC

D

BA

CO

NG

RU

EN

CE

ST

AT

EM

EN

T

ABCD = EFGH~

LMCBJK. Complete the following statements.

1. LC_____

2. KJ_____

3. JB_____

4. L_____

5. K_____

6. M_____

7. CML_____

8. KBJ_____

9. MLC_____

10. JKB_____

BK

CM

ML

B

C

J

KJB

CLM

JBK

MCL

Labeling an angle or a side Labeling an angle or a side in correct order is very in correct order is very

important.important.

Lets see if you Lets see if you can do it.can do it.

Lets label the Lets label the congruent partscongruent partsL

N M

P

Q R

N R

L P

M Q

NL RP

LM PQ

NM RQ

NLM RPQ

A T

S

B C

F

Now it’s you turn to Now it’s you turn to label all the congruent label all the congruent parts for the triangles.parts for the triangles.

A C

S F

T B

AS CF

ST FB

TA BC

AST CFB