Midsegments and SideSplitting Theorem

Front

What does the Side Splitter Theorem state?

Back

If a line is parallel to one side of a triangle and intersects the other two sides, then the ratios of the lengths of the segments created on those sides are equal.

Tags

CCSS.HSG.SRT.B.4

Front

If a line segment WY is parallel to side AB of triangle ABC, what can we say about the ratios of the segments?

Back

The ratios of the segments created by the intersection of WY with sides AC and BC are equal.

Tags

CCSS.HSG.SRT.B.4

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle.

Front

How does the length of a midsegment compare to the lengths of the sides of the triangle?

Back

The length of a midsegment is half the length of the side it is parallel to.

Front

If segment WX is a midsegment of triangle PQR, what is the relationship between WX and side PR?

Back

WX is parallel to PR and its length is half the length of PR.

Tags

CCSS.HSG.SRT.B.4

Front

What is the formula for the Side Splitter Theorem?

Back

Tags

CCSS.HSG.SRT.B.4

Front

In triangle ABC, if DE is parallel to BC and AD = 6, DB = 3, what is the length of DE?

Back

DE = 4.5 (using the Side Splitter Theorem).

Tags

CCSS.HSG.SRT.B.4

Front

What is the significance of parallel lines in the Side Splitter Theorem?

Back

Parallel lines create proportional segments on the intersecting sides of the triangle.

Tags

CCSS.HSG.SRT.B.4

Front

If segment AB is parallel to segment CD in triangle EFG, what can we conclude about the segments EF and FG?

Back

The segments EF and FG are divided proportionally by the parallel lines.

Tags

CCSS.HSG.SRT.B.4

Front

What is the relationship between the lengths of segments created by a transversal intersecting parallel lines?

Back

The lengths of the segments created by the transversal are proportional to the lengths of the segments on the other side.

Tags

CCSS.HSG.SRT.B.4