Q. 1345.0( 3 Votes )

# In each of the given pairs of triangles of Fig. 6.42, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

Answer :

**Formula Used/Theory:-**

ASA congruence criterion is in which 2 angles and a side between them are equal in both the triangles

(a) ∠A = ∠Q

But ∠B≠∠P

∴ Δ ABC and Δ PQR are not congruent

**Result:-** Δ ABC and Δ PQR are not congruent

(b) ∠ABD = ∠BDC

∠ADB = ∠DBC

BD = BD (common in both triangle)

∴ Δ ADB and Δ CBD are congruent by ASA

∆ADB ≅ ∆CBD

**Result:-** Δ ADB and Δ CBD are congruent by ASA

(c) ASA congruence criterion is in which 2 angles and a side between them are equal in both the triangles

∠X = ∠L

∠Y = ∠M

XY = ML

∴ Δ XYZ and Δ LMN are congruent by ASA

∆XYZ ≅ ∆LMN

**Result:-** Δ XYZ and Δ LMN are congruent by ASA

(d) → Angle sum property

Sum of all angles of triangle is 180°

By angle sum property

∠A + ∠B + ∠C = 180° ∠D + ∠E + ∠F = 180°

Equating both

We get;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

As ∠B = ∠F

∠A = ∠D

Cancelling out we get, ∠C = ∠E

∠C = ∠E

∠B = ∠F

BC = FE

∴ Δ ABC and Δ DFE are congruent by ASA

∆ABC ≅ ∆DFE

**Result:-** Δ ABC and Δ DFE are congruent by ASA

(e) In Δ PNO and Δ MNO

∠PNO = ∠MON

∠MNO≠∠PON

ON = ON (common in both triangles)

∴ Δ MNO and ΔPON are not congruent by ASA

**Result:-** ∴ Δ MNO and ΔPON are not congruent by ASA

(f) ∠D = ∠C

∠AOD = ∠COB

OD = CO

∴ Δ ADO and Δ BCO are congruent by ASA

∆ADO ≅ ∆BCO

**Result:-** Δ ADO and Δ BCO are congruent by ASA

Rate this question :

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.

NCERT - Exemplar Mathematics

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

NCERT - Exemplar MathematicsIn 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?

NCERT - Exemplar Mathematics

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?

NCERT - Exemplar Mathematics

State whether the statements are True or False.

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

NCERT - Exemplar Mathematics

Fill in the blanks to make the statements true.

In Fig. 6.25, ∆ARO ≅ ∆ ____PQO____

NCERT - Exemplar Mathematics

Fill in the blanks to make the statements true.

In Fig. 6.24, ∆ ____DRQ____ ≅ ∆PQR

NCERT - Exemplar Mathematics