Geometric proofs
Types of exercises: triangle congruence conditions, choose the justification, which data prove congruence?, a counterexample.
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Statement: "Any three segments shorter than 10 cm can form a triangle." Which answer is a counterexample, that is, shows that the statement is false?
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We want to justify: the base angles of an isosceles triangle are equal. Which sentence justifies it?
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The vertices of triangles ABC and KLM correspond like this: A to K, B to L, C to M. Which data are enough to show that these triangles are congruent?
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Two triangles are such that two sides and the angle BETWEEN them in one are equal to two sides and the angle BETWEEN them in the other. Which congruence condition shows that they are congruent?
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Statement: "Every quadrilateral with four right angles is a square." Which answer is a counterexample, that is, shows that the statement is false?
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We want to justify: the diagonals of a parallelogram bisect each other. Which sentence justifies it?
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The vertices of triangles ABC and KLM correspond like this: A to K, B to L, C to M. Which data are enough to show that these triangles are congruent?
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Two triangles are such that one side and the two angles AT ITS ENDS in one are equal to one side and the two angles at its ends in the other. Which congruence condition shows that they are congruent?
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Statement: "If two angles of a triangle are acute, then the triangle is acute." Which answer is a counterexample, that is, shows that the statement is false?
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We want to justify: an exterior angle of a triangle equals the sum of the two non-adjacent interior angles. Which sentence justifies it?
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