When two plane figures superpose each other, that is, when one figure is placed on top of the other, they are congruent.

Suppose a plane P1 is congruent to plane P2, then it is written or denoted as P1≅P2.

One line segment can be superimposed on top of another to see if the line segments are congruent. They must be congruent if they cover one other. If the lengths of two line segments are the same, they are congruent. When it comes to 2D shapes, they are congruent if they are of the same shape and size. The image cannot be bent, stretched, or twisted in any way.

Two angles with the same measurement are congruent.

If we overlay one triangle on top of the other. They must be congruent triangles to cover each other adequately.

In the demonstration of class 7 congruence of triangles:

• Each triangle's sides must be equal to the corresponding sides of another triangle.
• All of the angles in one triangle must be equal to the angles in the other triangle.
• All of a triangle's vertices must correspond to the vertices of another triangle.
• ∠A ↔ ∠F, ∠B ↔ ∠D and ∠C ↔ ∠E is the corresponding vertices.
• ∠A ↔ ∠F, ∠B ↔ ∠D and ∠C ↔ ∠E are the angles that correspond.
• AB ↔ FD, BC ↔ DE, and AC ↔ FE are the corresponding sides.

Remark: The corresponding relationships between two triangles are determined by the letters in the names of congruent triangles in their proper order. The two triangles don't need to be congruent if we alter it from ∆ABC ≅ ∆FDE to ∆BCA ≅ ∆FDE, because all of the corresponding sides, angles, and vertices must be the same.

Criteria for congruence of two triangles are:

(i) SSS Theorem

(ii) SAS Theorem

(iii) ASA Theorem

(iv) RHS Theorem

SSS Criteria for Congruence

If under a given correspondence, the three sides of 1 triangle are adequate to the three corresponding sides of another triangle, then the triangles are congruent.

SAS Criteria for Congruence

If two sides of a triangle and the angle between them are equal to two corresponding sides and the angle between them of another triangle under a correspondence, the triangles are congruent.

ASA Criteria for Congruence

The triangles are congruent if two angles and the included side of one triangle are equal to two similar angles and the included side of another triangle.

AAS Criteria for Congruence

If two triangles have the same pair of equivalent angles and opposite sides, they are congruent, according to the AAS Rule.

One of the internal angles in a right-angled triangle is 90 degrees. If two right triangles have the same shape and size, they are congruent. To put it another way, two right triangles are said to be congruent if the lengths of their respective sides and angles are the same.

1. Fill in the blanks to complete the following statements:

(a)If two line segments are the ____________, they are congruent.

Solution:- If two line segments are the same length, they are congruent.

(b) One of two congruent angles has a measure of70°, while the other has a measure of ________.

Solution:- One of two congruent angles has a measure of70°, while the other has a measure of 70°.

Because two angles with the same measure are said to be congruent. In addition, if two angles are congruent, they have the same measure.

(c) What we mean when we write ∠A = ∠B.

Solution: We mean m ∠A = m ∠B when we write ∠A = ∠B.

2. Give two examples of congruent shapes from everyday life.

Solution: Two real-life examples of congruent forms.

(i) Fan feathers of the same brand.

(ii) Chocolate size within the same brand.

(iii) Pen sizes from the same brand

3. Write all the matching congruent sections of the triangles if ΔABC ≅ ΔFED under the correspondence ABC ↔ FED.

Solution:-  When the sides and angles of two triangles are equal, they are said to be congruent.

All of the triangles' matching congruent parts are,

∠B ↔ ∠E, ∠A ↔ ∠F, ∠C ↔ ∠D

Correspondence between the two parties:

4. If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to

5. In the following, which congruence criterion do you use?

(a) Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

 

Solution:

According to the SSS congruence property, two triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle, according to the SSS congruence property.

ΔABC ≅ ΔDEF

(b) Given: ZX = RP

RQ = ZY

∠PRQ = ∠XZY

So, ΔPQR ≅ ΔXYZ

Solution:

According to the SAS congruence property, two triangles are congruent if one's two sides and included angle is equal to the other's two sides and included angle.

ΔACB ≅ ΔDEF

    1. What are the four tests of congruence in a triangle?

Answer: Conditions for Congruence of Triangles:

• SSS (Side-Side-Side)
• SAS (Side-Angle-Side)
• ASA (Angle-Side-Angle)
• AAS (Angle-Angle-Side)
• RHS (Right angle-Hypotenuse-Side)

     2. Is AAA a congruence theorem?

Answer: No, there is no AAA congruence theorem because when two triangles have equal corresponding angles, one of the two triangles can be an enlarged copy of the other.

     3. What are the criteria for the congruence of triangles?

Answer: When the three angles of one triangle are equal to the three angles of the other triangle, they are considered congruent. This is the SSS rule. When two angles and one side of the triangle are similar to the other triangle, then it is called the ASA rule. When two angles and other angles of one triangle are equal to the other sides of another triangle, it is called the SAS rule.

     4. How do you write congruent triangles?

Answer: This means that congruent triangles are identical duplicates of one another, and the sides and angles that coincide, known as corresponding sides and angles, are equal when they are put together. In the given figure, △ABC is congruent to △DEF. The symbol for congruence is ≅ and we write △ABC≅△DEF.

    5. What is the ASA congruence rule?

Answer: According to the ASA congruence rule, two triangles are congruent if two angles and the side included between them are equal to the corresponding angles. Between the other triangles, a side is formed.