A transversal intersects two parallel lines and forms eight angles. Which of the following statements is false?
a)alternative interior angles are always congruent.
b)corresponding angles are always congruent.
c)adjacent interior angles are always supplementary
d)exterior angles are always congruent
i eliminated a,c, and d. I think c is false because i don't think all adjacent interior angles add up to 180 degrees. Is this right?
A transversal intersects two parallel lines. If measure of one of the interior angles is 4 times the other, the measure of the smaller angle is
Yes, you are correct. Statement c) "Adjacent interior angles are always supplementary" is false. Adjacent interior angles are only supplementary when the transversal intersects two parallel lines. If the lines are not parallel, the adjacent interior angles may not add up to 180 degrees.
To determine which statement is false, let's review the properties of angles formed by a transversal intersecting two parallel lines.
When a transversal intersects two parallel lines, several pairs of angles are formed:
1. Vertical Angles: These are the angles opposite each other when two lines intersect. They are always congruent.
2. Corresponding Angles: These are pairs of angles that lie on the same side of the transversal and on the same side of the parallel lines. Corresponding angles are always congruent.
3. Alternate Interior Angles: These are pairs of angles that lie on the opposite sides of the transversal and on the inside of the parallel lines. Alternative interior angles are always congruent.
4. Alternate Exterior Angles: These are pairs of angles that lie on the opposite sides of the transversal and on the outside of the parallel lines. Alternative exterior angles are always congruent.
Now let's evaluate each statement:
a) Alternative interior angles are always congruent: This statement is true. Alternative interior angles are always congruent, so this statement is not false.
b) Corresponding angles are always congruent: This statement is true. Corresponding angles are always congruent, so this statement is not false.
c) Adjacent interior angles are always supplementary: This statement is also true. Adjacent interior angles are two angles that are adjacent to each other and on the same side of the transversal. They always add up to 180 degrees, making them supplementary. Therefore, this statement is not false.
d) Exterior angles are always congruent: This statement is false. Exterior angles formed by a transversal and parallel lines are not always congruent. The measure of the exterior angles varies depending on the specific configuration of the lines. Therefore, this statement is false, and it is the answer you are looking for.
In conclusion, the statement that is false is d) Exterior angles are always congruent.