Question

Given: ZA ZDEF and ZGHI ZDEF

Prove: m ZABC=mZGHI
a) ZABC
b) ZOEF
c) ZGH
d) mZGH

Answer 1

To prove that m∠ABC = m∠GHI, we need to show that the two angles are congruent to each other. Given that ZA ZDEF and ZGHI ZDEF, it means that angle ZDEF is a common angle of both triangles.

Step-by-step explanation:

To prove that m∠ABC = m∠GHI, we need to show that the two angles are congruent to each other.

Given that ZA ZDEF and ZGHI ZDEF, it means that angle ZDEF is a common angle of both triangles.

If angle ABC is congruent to angle DEF, and angle GHI is also congruent to angle DEF, by the Transitive Property of Congruence, angle ABC is congruent to angle GHI. Hence, their measures are equal by the definition of congruent angles.

Therefore, by the transitive property of congruence, we can conclude that m∠ABC = m∠GHI.