Question

Writing a Two-Column Proof

a) Given ZABC ZDEF and LGHI ZDEF
b) Prove mZABC = mZGHI
c) IR
d) ДАВС
e) ZDEF
f) LGHI
g) M_ABC
h) mZGHI

Answer 1

Using the transitive property of congruent triangles, we can effectively prove that m∡ABC = m∡GHI because ∡ABC is congruent to ∡DEF and ∡GHI is also congruent to ∡DEF, establishing that ∡ABC must be congruent to ∡GHI.

Step-by-step explanation:

Two-Column Proof

Based on the information provided, we are tasked with proving that m∡ABC = m∡GHI using a two-column proof. The information given suggests that ∡ABC is congruent to ∡DEF and also ∡GHI is congruent to ∡DEF. By the transitive property of congruent triangles, we can deduce that ∡ABC is congruent to ∡GHI, and therefore, their corresponding angles are equal. This means that their measures are also equal, which is what we aimed to prove:

1. Given that ∡ABC ≈ ∡DEF and ∡GHI ≈ ∡DEF.
2. By the Transitive Property of Congruence, if ∡ABC ≈ ∡DEF and ∡GHI ≈ ∡DEF, then ∡ABC ≈ ∡GHI.
3. Therefore, m∡ABC = m∡GHI, because corresponding angles of congruent triangles are equal.