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Given: [tex]L1[/tex] and [tex]L2[/tex] are supplements, [tex]L3[/tex] and [tex]L4[/tex] are supplements, and [tex]L1 = L4[/tex].

Prove: [tex]L2 = L3[/tex].

(Statements and Reasons provided)

Answer :

Final answer:

The problem demonstrates a geometric proof showing that if L1 and L2 are supplementary, L3 and L4 are supplementary, and L1 equals L4, then L2 must equal L3 due to the properties of supplementary angles and equality.

Explanation:

The question requires a proof involving supplementary angles. If L1 and L2 are supplementary, and L3 and L4 are supplementary, and it is given that L1 = L4, then we must prove that L2 = L3.

In geometry, supplementary angles are two angles whose measures add up to 180 degrees. Given that L1 and L2 are supplements, it follows that L1 + L2 = 180 degrees. Similarly, for L3 and L4 being supplements, we have L3 + L4 = 180 degrees. Since it is given that L1 equals L4, we can substitute L4 with L1 in the second equation, which gives us L3 + L1 = 180 degrees. Comparing this to the first equation, L1 + L2 = 180 degrees, we can see that both L2 and L3 must be equal since they are both being added to L1 to reach the total of 180 degrees.

Therefore, by the property of equality, where if a = b and b = c, then a = c, we have proven that L2 = L3.

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