When // lines are cut by a transversal, the corresponding angles are supplementary.
true or false ?
explain,
thanks !
True.
True.
When lines are cut by a transversal, the corresponding angles are formed on opposite sides of the transversal and in the same position relative to the lines. These corresponding angles are also known as "same-side interior angles."
According to the corresponding angles theorem, when a transversal cuts two parallel lines, the corresponding angles are congruent. However, when the lines are not parallel, the corresponding angles are still related. They are supplementary, meaning that the sum of their angles is equal to 180 degrees.
In other words, if you have a pair of corresponding angles, one angle measures x degrees, the other angle will measure 180-x degrees. This relationship holds true for all corresponding angles formed by the transversal cutting the lines.
True.
To understand why, let's first define what it means for two lines to be cut by a transversal. When two lines are intersected by a third line (known as a transversal) in a plane, several angles are formed.
Corresponding angles are a pair of angles that are formed on the same sides of the transversal and on the same or corresponding positions. These angles are found in matching or corresponding positions with respect to the transversal.
When a transversal intersects two parallel lines, the corresponding angles formed are congruent (having the same measure). But even when the lines are not parallel, the corresponding angles still have a special relationship.
The statement "corresponding angles are supplementary" means that the sum of any pair of corresponding angles formed by a transversal and two lines is equal to 180 degrees. In other words, if you add the measures of the two corresponding angles, the total will be equal to 180 degrees.
To prove this, you can use the properties of parallel lines and transversals or the rules of angles formed by intersecting lines. By studying the angles formed by the transversal, you can identify pairs of corresponding angles and find that their sum is always 180 degrees.