Question

50 Points!!! Explain the difference between consecutive interior angles, corresponding interior angles, and co-interior angles.

Answer 1

In geometry, consecutive interior angles are supplementary angles on the same side inside two lines crossed by a transversal, corresponding angles are in matching positions and equal when lines are parallel, and co-interior angles are supplementary angles on the same side inside parallels.

Step-by-step explanation:

The terms consecutive interior angles, corresponding angles, and co-interior angles are used in geometry to describe the relationships between angles when two lines are crossed by another line (the transversal).

• Consecutive interior angles are angles that are on the same side of the transversal and inside the two lines. They are also known as alternative interior angles. If the two lines are parallel, these angles are supplementary, meaning they add up to 180 degrees.
• Corresponding angles are angles that are in the same position at each intersection where the transversal crosses the two lines. If the lines are parallel, corresponding angles are equal.
• Co-interior angles, also known as same-side interior angles, are pairs of angles that are on the same side of the transversal and inside the two lines. They are supplementary if the lines are parallel.

Distinguishing between these types of angles is important for solving geometry problems, especially those involving parallel lines and transversals. Understanding these angle relationships helps in proving the properties of geometric figures and in solving for unknown angles.

Answer 2

Co-interior angles or Consecutive interior angles are the two angles that are on the same side of the transversal. Co-interior angles are the interior angles and it sums up to 180 degrees. It means that the sum of two interior angles, which are on the same side of transversal is supplementary. Co-interior angles resemble like in “C” shape and both the angles are not equal to each other. The co-interior angle is also known as the consecutive interior angles or the same side interior angles.Co-interior Angles

Co-interior Angle Theorem and Proof

Statement:

If the transversal intersects the two parallel lines, each pair of co-interior angles sums up to 180 degrees (supplementary angles).

Proof:

Co-interior Angles Proof

Let us consider the image given above:

In the figure, angles 3 and 5 are the co interior angles and angles 4 and 6 are the co-interior angles.

To prove: ∠3 and ∠5 are supplementary and ∠4 and ∠6 are supplementary.

Given that, a and b are parallel to each other and t is the transversal.

By the definition of linear pair,

∠1 and ∠3 form the linear pair.

Similarly, ∠2 and ∠4 form the linear pair.

By using the supplement postulate,

∠1 and ∠3 are supplementary

(i.e.) ∠1 + ∠3 = 180

Similarly,

∠2 and ∠4 are supplementary

(i.e.) ∠2 + ∠4 = 180

By using the corresponding angles theorem, we can write

∠1 ≅∠5 and ∠2 ≅ ∠6

Thus, by using the substitution property, we can say,

∠3 and ∠5 are supplementary and ∠4 and ∠6 are supplementary.

Hence, the co-interior angle theorem (consecutive interior angle) is proved.

The converse of this theorem is “if a transversal intersects two lines, such that the pair of co-interior angles are supplementary, then the two lines are parallel”.