Side Splitter Theorem

Front

What is the Side Splitter Theorem?

Back

The Side Splitter Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

If AB = 4, BC = 7, ED = 5, and DC = 8.75, is BD parallel to AE?

Back

Yes, BD is parallel to AE according to the Side Splitter Theorem.

Front

What is the formula to find the missing length using the Side Splitter Theorem?

Back

If a line divides two sides of a triangle proportionally, then a/b = c/d, where a and b are segments of one side, and c and d are segments of the other side.

Front

If a triangle has sides of lengths 6 and 9, and a line parallel to the base divides the other two sides into segments of lengths 4 and x, what is x?

Back

x = 6.75, using the proportion 6/9 = 4/x.

Front

What does it mean for two lines to be parallel in the context of triangles?

Back

Two lines are parallel if they never intersect and are equidistant from each other, which affects the proportionality of the segments created by a transversal.

Front

If a triangle has sides of lengths 10 and 15, and a line parallel to the base divides the other two sides into segments of lengths 5 and y, what is y?

Back

y = 7.5, using the proportion 10/15 = 5/y.

Front

How can you determine if two segments are proportional?

Back

Two segments are proportional if the ratio of their lengths is equal to the ratio of the lengths of another pair of segments.

Front

What is the significance of the Side Splitter Theorem in geometry?

Back

The Side Splitter Theorem helps in solving problems involving triangles and parallel lines, allowing for the calculation of unknown lengths.

Front

If a triangle has sides of lengths 8 and 12, and a line parallel to the base divides the other two sides into segments of lengths 4 and z, what is z?

Back

z = 6, using the proportion 8/12 = 4/z.

Front

What is a transversal in geometry?

Back

A transversal is a line that intersects two or more lines at distinct points, creating angles and segments that can be analyzed for proportionality.