1. Since WY is congruent to WZ, WYZ is isosceles. 2. This means that angle Y equals angle Z. 3. Since M is a midpoint, this means that YM is congruent to MZ. 4. Because both angle X and angle T are 90 degrees and the two bisectors meet at the midpoint, it follows that XY equals TZ. 5. By Side-Angle-Side, triangle YMX is congruent to triangle MZT. 6. Thus, MX is congruent to MT.