By which of the following criterion two triangles cannot be proved congruent?
A. AAA

B. SSS

C. SAS

D. ASA

You have to show that . In the following proof, supply the missing reasons.

You want to show that ∆ART ∆PEN,

(a) If you have to use SSS criterion, then you need to show

(i) AR =

(ii) RT =

(iii) AT =

(iv) AT =

(b) If it is given that ∠T = ∠N and you are to use

SAS criterion, you need to have

(i) RT = and (ii) PN =

(c) If it is given that AT = PN and you are to use

ASA criterion, you need to have

(i) ? (ii) ?

Which congruence criterion do you use in the following?

(a) Given: AC=DF

AB=DF

BC=EF

∆ABC ∆DEF

(b) Given: ZX=R

RQ=ZY

∠PQR = ∠XYZ

∆PQR ∆XYZ

(c) ∠MLN = ∠FGH

∠NML = ∠GFH

ML=FG

∆LMN ∆GFH

(d) Given: EB=DB

AE=BC

∠A = ∠C=90^o

∆ABC ∆CDB

In the following pairs of triangles of Fig. 6.47, the lengths of the sides are indicated along the sides. By applying SSS congruence criterion, determine which triangles are congruent. If congruent, write the results in symbolic form.

Without drawing the triangles write all six pairs of equal measures in each of the following pairs of congruent triangles.

(a) ∆STU ≅ ∆DEF

(b) ∆ABC ≅ ∆LMN

(c) ∆YZX ≅ ∆PQR

(d) ∆XYZ ≅ ∆MLN

In Fig. 6.49, it is given that LM = ON and NL = MO

A. State the three pairs of equal parts in the triangles NOM and MLN.

B. Is ∆NOM ≅ ∆MLN. Give reason?

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (Fig. 6.48).

A. State three pairs of equal parts in the triangles ABD and ACD.

B. Is ∆ABD ≅ ∆ACD. If so why?

State whether the statements are True or False.

In Fig. 6.28, two triangles are congruent by RHS.

Fill in the blanks to make the statements true.

In Fig. 6.25, ∆ARO ≅ ∆ ____PQO____

Fill in the blanks to make the statements true.

In Fig. 6.24, ∆ ____DRQ____ ≅ ∆PQR