By knowing that S is bisected by the line shown, we will conclude that PD = 8
So here we know that PC = 8, we also can see that:
- PCS is a right triangle
- PDS is a right triangle.
Notice that because the blue line bisects S, the angle at "S" on both of these right triangles is the same, and because both of these are right triangles, both must have a 90° angle.
Finally, if two angles are equal, then the 3 angles must be equal between these two triangles.
And notice that both of these triangles share one side, then:
Triangles we know for sure that triangles PCS and PDS have the same angles and one equal side.
This implies that the triangles are congruent, thus, the <u>measures of the corresponding sides must be the same.</u>
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Then the length of the shorter side of both triangles must be the same, in triangle PCS the short leg measures 8 units, then in triangle PDS the short leg, PD, also must measure 8 units.
So you are correct.
If you want to learn more about congruent triangles, you can read:
brainly.com/question/12077512
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