Question

What is the missing justification?

transitive property
reflexive property
symmetric property
substitution property

Answer 1

∠A ≅ ∠C (transitive property)

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.)

Answer 2

Option A is correct.

The missing justification is: Transitive property

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`