SME
Grade 10 Math · Geometry
Relationships within triangles: bisectors, medians, midsegments and inequalities
Use this for “D and E are midpoints of two sides, and the third side is 14. How long is the midsegment DE?”
Diagram
The midsegment DE joins the middles of AB and AC: it is parallel to BC and half as long.
This is an example. Type your own values to start a new problem.
DE
=
BC
2
CA
Side CA
example
AB
Side AB
example
Formulas
DE
=
BC
2
7
=
14
2
Assumptions
•
D and E are the midpoints of AB and AC; the segment DE joining them is a midsegment.
•
The midsegment is parallel to the third side BC and half as long: DE = BC ÷ 2.
•
Lengths are in any one unit.
Step-by-step
WE KNOW
BC = 14, CA = 12, AB = 10
FIND
midsegment DE (DE)
Step 1 · Find midsegment DE (DE)
Use DE = BC ÷ 2
The midsegment is half the third side.
DE
=
14
2
DE = 7
Check
Put the numbers back in. Both sides should match.
7
=
14
2
✓
Topic check
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