What is the parallel side splitter theorem?
What is the parallel side splitter theorem?
Side-Splitter Theorem If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Corollary to the Side-Splitter Theorem If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.
How do you prove the side splitter theorem?
(Side Splitter Theorem): If a line is parallel to a side of a triangle and intersects the other two sides, then this line divides those two sides proportionally. in this theorem does not necessarily connect the “midpoints” of the sides. 2. If 2 || lines are cut by a transversal, the corresponding angles are congruent.
What is the converse of the side splitter theorem does the converse have the same truth value as the original theorem?
A line parallel to a side of a triangle divides the other sides proportionally. (This fact is sometimes called the side-splitter theorem.) The converse of the side-splitter theorem is also true: a line that divides two sides of a triangle proportionally is parallel to the third side.
What do parallel lines mean in a triangle?
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
Why does the side splitter theorem work?
This theorem states that if a line is parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally. See the below figure. Then, because both triangles contain angle S, the triangles are similar by AA (Angle-Angle).
Why does the side-splitter theorem work?
What does side-splitter mean?
: one that is sidesplitting specifically : an exceedingly funny story or joke.
What does side splitter mean?
How do you prove two parallel lines?
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. If two lines are parallel to the same line, then they are parallel to each other.
What are two parallel lines?
Parallel Lines: Definition: We say that two lines (on the same plane) are parallel to each other if they never intersect each other, ragardless of how far they are extended on either side. Corresponding Angles are angles that are on the same side of the transversal and on the same side of each intersected line.
What are five ways to prove two lines are parallel?
Ways to Prove Two Lines Parallel
- Show that corresponding angles are equal.
- Show that alternative interior angles are equal.
- Show that consecutive interior angles are supplementary.
- Show that consecutive exterior angles are supplementary.
- In a plane, show that the lines are perpendicular to the same line.