Question

Complete the paragraph proof to prove the statement.
Given: ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF
Prove: m∠ABC = m∠GHI
We are given that angle ABC and are congruent, and that angle GHI and angle DEF are congruent. By the , the measure of angle ABC is equal to the measure of angle DEF, and the measure of angle GHI is equal to the measure of angle DEF. By the substitution property, the measure of angle ABC is equal to .

Answer 1

Two angles are said to be congruent if they have the same measure. The measure of angle ABC is congruent to the measure of angle DEF i.e. $\angle ABC = \angle D E F$

To prove that:

$\angle ABC \cong \angle G H I$

We have:

$\angle ABC \cong \angle D E F$ and $\angle GHI \cong \angle D E F$

$\angle D E F$ is common in the above equations.

This means that we can use substitution property

Substitution property states that:

If $a = b$ and $a = c$ then: $b =c$

Using the above as a reference,

The equations can be combined as:

$\angle ABC = \angle D E F$

Read more about congruent angles at:

https://brainly.com/question/10668231

Answer 2

Answer:

1) Statement) angle ABC is congruent to angle DEF

reason) Given

2) statement) angle GHI congruent to DEF

reason) given

3) statement) angle DEF is congruent to angle GHI

Reason) symmetric property

4) Statement) angle ABC is congruent to angle GHI

Reason) transitive property

5) statement) measure of angle ABC equals measure of angle GHI

Reason) definition of congruent angles

Step-by-step explanation:

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