The figure below is supposed to show three non-overlapping shapes, one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by '?' and completes the oval and the two triangles?
Show Hint
Check the oval's curve and both triangles' corners separately, the right piece must complete all three shapes without any overlap.
Step 1: Understand the question:
The picture shows an oval and two triangles that are cut by a white box marked with a "?".
We need to find which candidate piece, P, Q, R or S, fills that box so the oval and the two triangles look complete and whole.
Step 2: Set up the matching rule:
A correct piece must do two things at once.
It must carry a curved edge that continues the visible part of the oval smoothly, with no sudden bend or gap, and it must carry a small triangular corner that lines up with the cut edge of the triangle above the box, at the same slant and size.
Step 3: Check option (A) P:
In P, the curved patch sits at the same height and size as the visible oval edge, and its curve bends the same way, so it continues the oval without a jump.
The small triangle piece in P also lines up at the same angle as the cut corner of the triangle in the main figure, and the lower triangle in P matches the size and slant of the triangle piece shown below the box.
So P completes all three shapes at once.
Step 4: Check option (B) Q:
In Q, the small triangle piece points the wrong way compared to the cut edge of the triangle in the main figure, so the corner does not meet up cleanly.
This breaks the triangle even though the curve part may look close.
Step 5: Check option (C) R:
In R, the lower triangle piece is turned to a different slant than the one shown below the box in the main figure.
This means the second triangle does not close up properly, so R is not correct.
Step 6: Check option (D) S:
In S, the curved patch is much bigger than what is needed, more like a half circle than a small piece of an oval.
Using S would make the oval too large and would even overlap the triangle next to it, which breaks the non-overlapping shapes condition given in the question.
Final Answer:
Only option P continues the oval's curve and both triangles' edges correctly without any overlap or mismatch.
\[ \boxed{\text{P}} \]
