in geometry, for (in this case) triangles to be congruent they must be the same size, corresponding angle measures, and side lengths.
the little ticks on lines and angles are used to show congruence. For instance, if two lines both have two tick marks that means they are congruent or if an two angles each had one tick then it is saying they are congruent.
so for the top right: line UV = line XY (they’re both 6.5) line TU = line WX (they’re both 3) line TV = line WY (they’re both 7) so all the proper side lengths are congruent
angle VTU = angle YWX (they both have one tick mark to show congruence) angle TUV = angle WXY (they both have three tick marks to show congruence) angle UVT = angle XYW (they both have two tick marks to show congruence) so all the proper angle measurements are congruent
therefore triangle TVU is congruent to triangle WYX
For the bottom right triangles: line EF = line QR (they both have two tick marks to show congruence) line DE = line PQ (they both have one tick mark to show congruence) line DF = line PR (they both have three tick marks to show congruence) so the proper side lengths are congruent
angle DEF = angle PQR (as it is given they are both 90°) angle EFD = angle QRP (they both have two tick marks to show congruence) angle FDE = angle RPQ (they both have one tick mark to show congruence) so all the proper angle measurements are congruent
therefore triangle DFE is congruent to triangle PRQ
