If two triangles are congruent, which of the following statements must be true? Check all that apply.A.The triangles have the same size, but not the same shape.B.The corresponding sides of the triangles are congruent.C.The corresponding angles of the triangles are congruent.D.The triangles have the same size and shape.
Question
If two triangles are congruent, which of the following statements must be true? Check all that apply.A.The triangles have the same size, but not the same shape.B.The corresponding sides of the triangles are congruent.C.The corresponding angles of the triangles are congruent.D.The triangles have the same size and shape.
Solution
The correct statements are:
B. The corresponding sides of the triangles are congruent. This is true because congruent triangles have all sides of equal length.
C. The corresponding angles of the triangles are congruent. This is also true because congruent triangles have all angles of equal measure.
D. The triangles have the same size and shape. This is the definition of congruent triangles. They are identical in size and shape.
Statement A is incorrect. Congruent triangles have both the same size and shape, not just the same size.
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