- Define midpoints, congruent, and bisectors.
- Use the Segment Addition Postulate to find lengths of segments.
- Use midpoints to find the lengths of segments.
Congruent Line Segments
One of the most important words in geometry is congruent. This term refers to geometric objects that have exactly the same size and shape. Two segments are congruent if they have the same length.
Congruent objects have the _______________________ size and shape.
2. When we draw congruent segments, we use tic marks to show that two segments are congruent.
3. If there are multiple pairs of congruent segments (which are not congruent to each other) in the same picture, use two tic marks for the second set of congruent segments, three for the third set, and so on. See the two following illustrations:
- The geometric symbol for congruent is ____________.
How could you write this statement three different ways?
Now that you understand congruent segments, there are a number of new terms and types of figures you can explore.
A segment midpoint is a point on a line segment that divides the segment into two congruent segments. So, each segment between the midpoint and an endpoint will have the same length.
- A segment midpoint splits a segment into two _________________________ parts.
In the diagram below,
There is even a special postulate dedicated to midpoints.
Segment Midpoint Postulate
Any line segment will have exactly one midpoint—no more, and no less.
1. Why can there only be one midpoint?
2. How would you explain your answer above to a person who thought there could be three midpoints on one line segment?
Because a segment midpoint divides the segment into two congruent segments, you can use the midpoint to find the measure of a line segment.
Now that you know how to find midpoints of line segments, you can explore segment bisectors.
A bisector is a line, segment, or ray that passes through a midpoint of another segment.
You probably know that the prefix “bi-” means two (think about the two wheels of a bicycle). So, a bisector cuts a line segment into two congruent parts.
- A bisector cuts a segment into two ___________________________ parts.
- A bisector passes through a line segment’s ___________________________.
Segment Addition Postulate
The measure of any line segment can be found by adding the measures of the smaller segments that comprise it.
That may seem like a lot of confusing words, but the logic is quite simple:
- You can _________________ together all parts of a line segment to get the length of the entire segment.
Because of the Segment __________________________ Postulate, you can simply add the two parts of the segment together to get the total length of the line segment.
You can also use the Segment Addition Postulate to find missing measures of line segments within a larger line segment.
Why or why not? Explain.