References will be made to the attachment.two shapes are considered congruent to each other if they are of the same shape and same size.rigid motions include: - translations (shifting or moving the shape)- reflections- rotations (orientation)when you do rigid motions to a shape, there are no changes to the shape or size of that shapes. so rigid motions can be used to check for congruence.basically, the question is asking you to see what kind of translations, reflections, and rotations can you do to either one of the triangle to get it to the exact orientation of the other triangle.see figure 1. that is the starting situation.if you examine δjms (the triangle with labeled points j, m and s), you can see that if you rotate it somehow and then move (translate) the triangle, you can get it to the same exact place as the other triangle, δdpw.(clockwise rotations are considered negative, while counterclockwise rotations are considered positive.)see figure 2. if you rotate the triangle
about point j at
, then you'll get that result. (rotating about a point means the same as rotating around a point. so if you rotate the triangle 90 degrees clockwise around point j, you will get the resulting triangle in figure 2.)then, after rotating, if you translate δj'm's' 1 unit right and 5 units up, you will get the triangles overlapping.and when they are overlapping, they will have the same exact shape, which means that the two triangles are congruent.so we just used rigid motions to verify that the shapes are congruent.the congruency statement: δjms ≅ δdpw