Important Questions: Congruence of Triangles - Class 7 MCQ

According to the question, the triangles formed are right angled triangles, as shown in the figure. 

So,  Δ ADB ≌ Δ ADC (R.H.S. property)

Line segments of equal length are congruent.

In the given figure,AD = BC,AC = AC,  and ∠DAC = ∠BCA
(∵ AD||BC alternate angles)
By S.A.S. theorem ΔABC≅ΔCDA  
So, AB=DC.
(Corresponding parts of congruent triangles.)

  
In ΔPQR and ΔXYZ. ∠P = ∠X = 50^o PQ = XY  and PR  =XZ. 
∴ Δ PQR ≅ Δ XYZ (S.A.S. property)

The correct statement is:

Two triangles are said to be congruent if two sides and included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle.

Hence, statement A is false and statement R is true.

Two triangles are congruent when they are of the same shape and size , if any one of them is made to superpose on the other , it will cover exactly .Since both are equal , they cannot be smaller or larger. 

Corresponding parts of congruent triangles are equal.
So, PQ = AB = x cm, QR = BC = y cm and RP = CA = z cm.

Corresponding sides in ΔABD and ΔCBD.

Since ΔABD  and  ΔCBD  are  congruent, ∠ADB=∠CDB 
(Corresponding parts of congruent triangles).⇒ BD bisects ∠ADC

We have AB=AC.Angles opposite to these sides will also be equal. So angles opposite to these sides are angle and angle c. So angle b and angle c are equal.

Two triangles are said to be congruent by SAS criterion if and only if two sides and angle between them of one triangle are equal to the two sides and angle between them of another triangle.

Hence. if ∆ ART ≅ ∆ PEN by SAS criterion, and if it is given that ∠T = ∠N by SAS criterion, then

(i) RT = EN

(ii) PN = AT

BC is the hypotenuse of the given triangles. Whose measure must be known.

A.A.A. criterion does not exist.

If the three angles of a triangle are congruent to corresponding angles of the other, it is an enlarged copy of the triangle.

 corresponds to 

 corresponds to   [Note that  corresponds to PR.]