The adjacent angles of a rhombus have equal measures, find the measures of all the angles. Can you say that the given rhombus is also a square? Why
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They are not, unless they are all right, i.e. unless the rhombus is a square. Just look at an elongated rhombus; surely you see that its angles are not all equal!
What is true is that opposite angles are equal. That’s just because e.g. triangles ABC and ADC in our drawing have sides AB=AD, BC=CD and AC=AC, so that they are congruent and angles ABC = ADC.
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