Question

STATE AND PROVE THE CORRESPONDING ANGLE THEOREM​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

The Corresponding Angles Theorem states:

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Step-by-step explanation:

Proof:

=> Assume L and M are parallel, prove corresponding angles are equal.

Assuming L||M, let's label a pair of corresponding angles α and β. We know that angle γ is supplementary to angle α from the straight angle theorem (because T is a line, and any point on T can be considered a straight angle between two points on either side of the point in question). Note that β and γ are also supplementary, since they form interior angles of parallel lines on the same side of the transversal T (from Same Side Interior Angles Theorem).

Therefore, since γ = 180 - α = 180 - β, we know that α = β. This can be proven for every pair of corresponding angles in the same way as outlined above.

<= Assume corresponding angles are equal and prove L and M are parallel.

Assuming corresponding angles, let's label each angle α and β appropriately. By the straight angle theorem, we can label every corresponding angle either α or β.

For example, we know α + β = 180º on the right side of the intersection of L and T, since it forms a straight angle on T. Consequently, we can label the angles on the left side of the intersection of L and T α or β since they form straight angles on L.

Since, as we have stated before, α + β = 180º, we know that the interior angles on either side of T add up to 180º. By the same side interior angles theorem, this makes L || M.