ASA, SAS,AAS,SSS

Ms. Anna Carmela Lavin

TRIANGLE

Characteristics

• Has three sides and

three angles

• The three angles

sums up to 180𝟎

Name the Corresponding

sides and angles

Answer:

According to side 1. 𝑫𝑬 ≅ 𝑨𝑩2. 𝑩𝑪 ≅ 𝑬𝑭3. 𝑨𝑪 ≅ 𝑫𝑭

Answer:

According to angles 1. < 𝑨 ≅ < 𝑫2. < 𝑩 ≅< 𝑬3. < 𝑪 ≅ < 𝑭

KEY WORDS

1.TRIANGLE

2. CORRESPONDING

3. CONGRUENT

Congruence

of a Triangle

}Ways to prove that Triangles are Congruent

SSS CONGRUENCE POSTULATE

Three sides of one triangle are

congruent to the three sides of another

triangle

R

PS

Q

U

T

ΔSTUΔPQR

Congruent or Not

Congruent

P

S

T

G

L

M

Congruent or Not

ΔLGMΔPST

Not Congruent

Congruent or NotD

E

G

F

ΔDEF ΔGEFCongruent

SAS CONGRUENCE POSTULATE

If two sides and the included angle of

one triangle are congruent to two sides

and the included angle of another

triangle

Congruent or Not

ΔABC ΔDEF

Congruent

Congruent or Not

ΔAPQ ΔBQP

Not Congruent

Congruent or Not

ΔMPN ΔQSR

Congruent

ASA CONGRUENCE POSTULATE

If two angles and the included side of

one triangle are congruent to the two

angles and the included side of another

triangle

Congruent or Not

ΔPQR ΔTSRCongruent

Congruent or Not

Congruent

Congruent or Not

ΔABC ΔDEF

Not Congruent

SAA THEOREM

If the two angles and the nonincluded

side of one triangle are congruent to

two angles and the nonincluded side of

another

Congruent or Not

Not Congruent

Congruent or Not

Congruent

Congruent or Not? Explain

Not Congruent

Congruent or Not? Explain

Congruent by SAA

Congruent or Not? Explain

Congruent by ASA

Congruent or Not? Explain

Congruent by SAS

Congruent or Not? Explain

Not Congruent

Congruent or Not? Explain

Not Congruent

Algebraic Application

L

M N

G F

H

800

(2x)0

Congruent or Not? Why?

Find x?

L

MN

X

Y

Z

510

(4x)0

Algebraic Application

650

Congruent or Not?

Find x?

Algebraic Application

(4x-2) cm

22 cm

Congruent or Not?

Find x?

Algebraic Application

N

M

K

J

500

Congruent or Not?

Find x and y?

y

12

x+9

Algebraic Application

L

M N

S R

Q

2x+11

3x+9

y+100

(2y− 40)0

Congruent or Not?

Find x and y?

Something to think

1. Are all isosceles congruent?

2. Are all right triangles congruent?

3.Are all equilateral triangles congruent?

4. Can congruence be determined without measurements?

Activity

Congruent or Not?

Find x and y?

3𝑥 600

Activity

N

M

K

J

L

GIVEN: ∆𝑱𝑳𝑲 ≅ ∆𝑵𝑳𝑴

IF m< 𝑱𝑲𝑳 = 𝟔𝟔𝟎, then m< 𝑵𝑴𝑳 = ?

IF MN=15 in, then KJ = ?