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CONGRUENT

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CONGRUENT

TRIANGLES

D

A

E

B

F

C

Similar triangles are triangles that have the same shape and the same size.

ABCDEF

When we say that triangles are congruent there are several repercussions that come from it.

AD

BE

CF

Six of those statements are true as a result of the congruency of the two triangles. However, if we need to prove that a pair of triangles are congruent, how many of those statements do we need? Because we are working with triangles and the measure of the angles and sides are dependent on each other. We do not need all six. There are three special combinations that we can use to prove congruency of triangles.

1. SSS Congruency Theorem

3 pairs of congruent sides

2. SAS Congruency Theorem

2 pairs of congruent sides and congruent angles between them

3. ASA Congruency Theorem

2 pairs of congruent angles and a pair of congruent sides

A

D

13

13

5

5

B

F

C

E

12

12

1. SSS Congruency Theorem

3 pairs of congruent sides

ABC DFE

G

L

5

5

70

K

J

H

70

I

7

7

2. SAS Congruency Theorem

2 pairs of congruent sides and congruent angles between them

mH = mK = 70°

GHI LKJ

G

L

5

5

K

J

H

50

I

7

7

50

The SAS Congruency Theorem does not work unless the congruent angles fall between the congruent sides. For example, if we have the situation that is shown in the diagram below, we cannot state that the triangles are congruent. We do not have the information that we need.

Angles I and J do not fall in between sides GH and HI and sides LK and KJ respectively.

M

Q

70

70

50

50

N

R

P

O

7

7

3. ASA Congruency Theorem

2 pairs of congruent angles and one pair of congruent sides.

mN = mR

MNO QRP

mO = mP

T

X

Y

34

34

34

34

13

59

59

13

87

59

Z

S

U

It is possible for two triangles to be congruent when they have a pair of congruent angles and a pair of congruent sides given but another pair of angles that are not congruent. It is possible that the non-congruent angles are not corresponding and if you calculate the third angle of one of the triangles, you may find that it is congruent to the angle

13

13

mT = mX

mS = 180- (34 + 87)

mS = mZ

mS = 180- 121

mS = 59

TSU XZY

la fin

КОНЕЦ

τέλοσ

final

The end

KATAPUSAN

finito

ﭙﺎﻴﺎﻥ

sof