Symmetry, SSS, AAS reveal congruent triangles: AXP ≅ HMZ, PXS ≅ DHS, ASD ≅ HMX, MSP ≅ ZMD.
There are multiple pairs of congruent figures in the image. Here are some possible congruence statements:
ΔAXP ≅ ΔHMZ:This is because the line segment SD is a line of symmetry for the figure. A line of symmetry divides a figure into two congruent halves. In this case, ΔAXP and ΔHMZ are the two congruent halves.
ΔPXS ≅ ΔDHS:This is because of the SSS (side-side-side) congruence postulate. The sides PX, XS, and PS of ΔPXS are congruent to the sides DH, HS, and DS of ΔDHS, respectively.
ΔASD ≅ ΔHMX:This is also because of the SSS congruence postulate. The sides AS, SD, and DA of ΔASD are congruent to the sides HM, MX, and HX of ΔHMX, respectively.
ΔMSP ≅ ΔZMD: This is because of the AAS (angle-angle-side) congruence postulate. Angles ∠MSP and ∠ZMD are congruent, and sides MS and MZ are congruent. Additionally, the included sides SP and ZD are congruent.