Question

Which of the following represents the symmetric property of congruence? Question 7 options: A) If ≅ and ≅ , then ≅ B) If ≅ , then ≅ C) ≅ D) If ≅ , then ≅

Answer 1

The symmetric property of congruence is:

If ∠A ≅ ∠B, then ∠B ≅ ∠A.

If, AB ≅ CB, then CB ≅ AB.

Explanation:

Two triangles are said to be congruent if they have the same three sides and the same three angles, not necessarily the same sides or the same angles are equal.

The properties of congruence are:

• Reflexive property:

For all angles A, ∠A ≅ ∠A. That is, all angles are congruent to themselves.

If AB is side of a triangle then, AB ≅ AB.

• Symmetric Property:

For any angles A and B if, ∠A ≅ ∠B, then ∠B ≅ ∠A.

For sides AB and CB of a triangle if, AB ≅ CB, then CB ≅ AB.

• Transitive property:

For any angles A, B and C if, ∠A ≅ ∠B, and ∠B ≅ ∠C then ∠A ≅ ∠C.

For sides AB, CB and CA of a triangle if, AB ≅ CB, and CB ≅ CA, then AB ≅ CA.

Thus, the symmetric property of congruence is:

If ∠A ≅ ∠B, then ∠B ≅ ∠A.

If, AB ≅ CB, then CB ≅ AB.