To determine which statement could be proved with the help of a figure, it is useful to consider the properties or theorems commonly represented in geometric diagrams. Here’s a brief analysis of each option:
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The base angles of an isosceles triangle are congruent. - This is a well-known property of isosceles triangles and can be proven with a figure illustrating an isosceles triangle.
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A line connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. - This is known as the midsegment theorem and can also be illustrated and proved using a triangle with its midpoints.
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Two triangles are similar if they have two pairs of congruent angles. - This is also a known theorem in geometry and can be shown with appropriate figures of triangles with angle measurements.
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The sum of the interior angles of a triangle equals 180°. - This is a fundamental property of triangles that can be demonstrated using geometric figures, such as by drawing parallel lines through one angle.
All four statements could potentially be proved with the help of a figure, but if you were to select one based on typical properties illustrated in basic geometric figures, the first statement ("The base angles of an isosceles triangle are congruent") is a straightforward and commonly illustrated theorem.
Therefore, while all options could be proven with figures, the most directly relevant to a basic triangle figure would be the first statement regarding the base angles of an isosceles triangle.
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