Question

What is the missing justification?
transitive property
reflexive property
symmetric property
substitution property

Answer 1

Answer:

Option A is correct.

The missing justification is: Transitive property

Step-by-step explanation:

Given:  $\angle A \cong \angle B$ ,   $\angle C \cong \angle B$

Symmetric property of equality states the if for all real values of x , y

if x =y then, y =x.

Then, by symmetric property of equality:

we can write  $\angle C \cong \angle B$ as

$\angle B \cong \angle C$

Transitive property of equality states that if we have the two things that are equal to each other and the second thing is equal to a third thing.

i.e, if a =b and b =c

then a =c

By transitive property of equality:

if  $\angle A \cong \angle B$ and $\angle B \cong \angle C$

then;

$\angle A \cong \angle C$                      ......[1]

Congruent angle states that the angles have exact the same measure

Therefore, by definition of congruent angles in [1] we have;

$m\angle A = m \angle C$

Answer 2

Answer:

∠A ≅ ∠C (transitive property)

Step-by-step explanation:

Given : Some statements

We have to choose the correct justification for the missing justification from the given options.

Consider ,

Since, given ∠A ≅ ∠C and  ∠C ≅ ∠B  

then ,      ∠B ≅ ∠C (BY SYMMETRIC PROPERTY)  

Also,

Using transitive property ,

If A= B and B = C then A = C  

Thus, ∠A ≅ ∠C and  ∠C ≅ ∠B  

Then ∠A ≅ ∠C (transitive property)

Thus, m∠A = m∠C (definition of similar triangles.)