![]() ![]() Now let's repeat the process for two lines that are parallel, say Now if you take a look back at all six proofs, you'll notice something interesting: ∠8 because an angle supplementary to a second angle must be supplementary to any other angle of the same measure. ![]() ![]() ∠8 (obvious from the diagram), so ∠1 supp. ![]() Using the same numbered diagram, we see that ∠1 ≅∠5 by the corresponding angle postulate, and ∠5 supp. Exterior angles on the same side are supplementary ∠5 because an angle supplementary to a second angle must be supplementary to any other angle of the same measure.Ħ. Using the numbered diagram above, we see that ∠1 ≅∠5 by the corresponding angle postulate, and ∠4 is supplementary to ∠1 (obvious from the diagram). Interior angles on the same side are supplementary Therefore alternate exterior angles are congruent.ĥ. (Figure ↑) $\angle 1 \cong \angle 5$ by the corresponding angle postulate, and $\angle 5 \cong \angle 7$ because vertical angles are congruent, therefore $\angle 1 \cong \angle 7$ by substitution of $\angle 7$ for $\angle 5$ in the first expression. Therefore alternate interior angles are congruent. (Figure ↑) $\angle 1 \cong \angle 5$ by the corresponding angle postulate, and $\angle 1 \cong \angle 3$ because vertical angles are congruent, therefore $\angle 3 \cong \angle 5$ by substitution of $\angle 3$ for $\angle 1$ in the first expression. ![]()
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