Question

Which of the following represents the symmetric property of congruence?

Question 3 options:

A)

If ≅ , then ≅

B)

If ≅ , then ≅

C)

≅

D)

If ≅ and ≅ , then ≅

Answer 1

The symmetric property of congruence is represented by Option B: If AB ≡ CD, then CD ≡ AB, aligning with the principle that if one quantity equals another, the second equals the first as well.

Step-by-step explanation:

The symmetric property of congruence states that if one geometric figure is congruent to another, then the second is also congruent to the first. This is a reflection of the more general symmetric property of equality in algebra, which states that if one quantity equals another, the second equals the first as well.

Looking at the provided options, the one that represents the symmetric property of congruence is:

Option B: If AB ≡ CD, then CD ≡ AB.

This option correctly reflects the symmetric property, which can be written as if p ≡ q, then q ≡ p where p and q are geometric figures or algebraic expressions.

Answer 2

The symmetric property of congruence is:

If ∠A ≅ ∠B, then ∠B ≅ ∠A.

If, AB ≅ CB, then CB ≅ AB.

Step-by-step 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.