Reflective sets of angles
Given: <ABC is congruent to <EFG
<1 is congruent to <3
Prove: <2 is congruent to <4
Statements: Reasons:
1.) <ABC is congruent to <EFG 1.) Given
(m<ABC is congruent to m<EFG)
<1 is congruent to <3
(m<1 is congruent to m<3)
Please help me finish the proofs!
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2.) m<ABC = m<EFG 2.) Definition of congruence
3.) m<1 = m<3 3.) Definition of congruence
4.) m<ABC = m<EFG = m<1 = m<3 4.) Transitive property of equality
5.) <2 is congruent to <4 5.) Definition of congruence
To finish the proof, we can use the Transitive Property of Congruence. Here's how you can fill them in:
Statements: Reasons:
1.) <ABC is congruent to <EFG 1.) Given
(m<ABC is congruent to m<EFG)
<1 is congruent to <3
(m<1 is congruent to m<3)
2.) <1 is congruent to <ABC 2.) Symmetric Property of Congruence
(m<1 is congruent to m<ABC)
3.) <3 is congruent to <EFG 3.) Transitive Property of Congruence
(m<3 is congruent to m<EFG)
4.) <ABC is congruent to <3 4.) Transitive Property of Congruence
(m<ABC is congruent to m<3)
5.) <3 is congruent to <4 5.) Given
(m<3 is congruent to m<4)
6.) <ABC is congruent to <4 6.) Transitive Property of Congruence
(m<ABC is congruent to m<4)
7.) <1 is congruent to <4 7.) Transitive Property of Congruence
(m<1 is congruent to m<4)
8.) <2 is congruent to <4 8.) Transitive Property of Congruence
(m<2 is congruent to m<4)
Therefore, we have proven that <2 is congruent to <4 using the given information and properties of congruence.