- Place the isosceles triangle ΔXYZ on the coordinate plane with vertex X at the origin (0, 0) and base XZ along the x-axis.
- Since XZ is the base and W is its midpoint, place Z at (2a, 0) so that W, the midpoint, has coordinates ((0 + 2a)/2, (0 + 0)/2) = (a, 0).
- Place the vertex Y, which forms the vertex angle, at (a, b), ensuring it lies directly above the midpoint W on the perpendicular bisector of the base XZ.
- The segment YW connects Y(a, b) to W(a, 0). Since both points have the same x-coordinate, YW is a vertical line segment.
- The segment XZ connects X(0, 0) to Z(2a, 0). Since both points have the same y-coordinate, XZ is a horizontal line segment.
- A vertical line is always perpendicular to a horizontal line. Therefore, YW ⊥ XZ.
- Thus, the segment joining the vertex angle of an isosceles triangle to the midpoint of its base is perpendicular to the base.
Parent Tip: Review the logic above to help your child master the concept of triangles and coordinate proof worksheet.
