Question

if a transversal intersects two parallel lines , then each pair of corresponding angles is equal

Answer 1

Answer:

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.