This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
Congruent
let's determine if these pairs of shapes are congruent.
First, let's clarify the definitions provided in the image:
The question asks whether the pairs of shapes are congruent or not congruent. If shapes are similar but not the same size, they are considered "not congruent."
Step 1: Analyze each pair of shapes based on their exact match in shape and size.
a. The two parallelograms appear to be identical in both shape and size.
b. The two right-angled triangles appear to be identical in both shape and size.
c. The first shape is a plus sign, and the second is an 'X' shape. They are clearly different shapes.
d. The two quadrilaterals are different in both shape and size.
e. The two rounded rectangles are the same shape but are clearly different in size.
f. The two octagons are the same shape but are clearly different in size.
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They are exactly the same in shape and size. Similar shapes have equal angles but not equally long sides.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.