Cogito
Geometry · Chapter 4 · Lesson 3
The Side-Splitter Theorem
A parallel cut divides both sides in the same ratio.
11 problems · about 22 minutes · G-SRT.B.4, G-CO.C.10
What this lesson teaches
The student applies the side-splitter theorem and the midsegment result.
- A line parallel to one side cuts the other two in the same ratio.
- It works because the parallel creates a similar triangle.
- A midsegment joins two midpoints and is half the third side.
Warm Up
Straightforward practice. Get the method working first.
4 problemsThird side 16. Midsegment?
Answer 8
Why 8.
Third side 20. Midsegment?
Answer 10
Why Half.
Midsegment 6. Third side?
Answer 12
Why Double.
Cut divides 4 and 8, other side 5 and x. What is x?
Answer 10
Why 1 to 2.
Build It Up
The same ideas with more to keep track of.
3 problemsCut divides 6 and 6, other side 9 and x. What is x?
Answer 9
Why Equal halves.
Is a midsegment parallel to the third side? 1 for yes, 0 for no.
Answer 1
Why Always.
Third side 9. Midsegment, as a decimal?
Answer 4.5
Why Half of 9.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsCut divides 2 and 10, other side 1 and x. What is x?
Answer 5
Why 1 to 5.
Does the parallel line create a similar triangle? 1 for yes, 0 for no.
Answer 1
Why Equal corresponding angles.
The Midsegment: The third side is 14. How long is the midsegment?
Answer 7
Why 7.
The Ratio: A cut divides one side 2 and 4, the other 3 and x. What is x?
Answer 6
Why 6.