CONGRUENT TRIANGLE

FACTS

S.S.S

If three sides of one triangle are

exactly the same as the three sides

of another triangle,

then they are congruent.

S.S.S

S.A.S

●If two

sides and the included angle

of one triangle and two sides & the included angle of another triangle

are exactly the same, then they are congruent.

●S.A.S

A.A.S

●

If two angles and a

side of one triangle are exactly the same

as two angles and the

corresponding side of another

triangle, then they are congruent.

●

A.A.S

R.H.S

If a right-angle, a hypotenuse & a side are exactly the same as the right-angle, hypotenuse and corresponding side, then they are congruent

R.H.S

CONGRUENT PROOFS(NOT DRAWN TO SCALE)

Prove that ABC DEF Prove that PQR STU

A

B

C D

E

F

22º

P

Q

R

4cm

4cm

5cm

5cm

2cm 2cm

S U

T

25mm

25mm

17mm

17mm

22º

CONGRUENT PROOFS(NOT DRAWN TO SCALE)

Prove that ABC DEF Prove that PQR STU

AB = DE = 4cm (given) S PQ=ST = 17mm (given) SBC = EF = 5cm (given) S PQR= STU = 22º (given) AAC = DF = 2cm (given) S QR = TU = 25mm (given) S ABC DEF (SSS) PQR STU (SAS)

4cm

4cm

5cm

5cm

2cm 2cm

CONGRUENT PROOFS(NOT DRAWN TO SCALE)

Prove that ABC DEF Prove that PQR STU

AB = DE = 4cm (given) S PQ=ST = 17mm (given) SBC = EF = 5cm (given) S PQR= STU = 22º (given) AAC = DF = 2cm (given) S QR = TU = 25mm (given) S ABC DEF (SSS) PQR STU (SAS)

22º

P R U

25mm

17mm

A

B

C D

E

F

25mm

17mm

22º

Q T

CONGRUENT PROOFS(NOT DRAWN TO SCALE)

Prove that QAW RDF Prove that GHI JKL

25m 25m

33º 33º

71º71ºA W

Q R

D F

3km

3km

G J

H I K L2km 2km

CONGRUENT PROOFS(NOT DRAWN TO SCALE)

Prove that QAW RDF Prove that GHI JKL

AQW = DRF = 33º (given) A GHI= JKL = 90º (given)

R AWQ = DFR = 71º (given) A GI= JL = 3km (given) HAW = DF = 25m (given) S HI = KL = 2km (given) S QAW RDF (AAS) GHI JKL(RHS)

25m

33º 33º

A W F

3km

3km

H 2km 2km71º71º

Q RG J