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Need help!! Geometry. Question says: Match the conclusion on the right with the given information. Explain your reasoning.

Need help!! Geometry. Question says: Match the conclusion on the right with the given-example-1
User Foslock
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The answers are matched based on geometric principles: isosceles triangles (8-A and 9-D), angle-side-angle inequality (10-B), and parallelograms (11-C) properties.

The image presents geometric problems, requiring matching of given information with appropriate conclusions.

For problem 8, "AB = BC, m∠1 = m∠2," option A is correct because if two sides and their included angles are equal, the opposite angles will also be equal due to the properties of an isosceles triangle.

In problem 9, "AD ≅ EC, AD = CD," option D matches as it implies that triangle AED is an isosceles triangle and thus AE cannot be equal to EC.

For problem 10, "m∠9 < m∠10, BE = ED," option B fits as angle-side-angle inequality indicates that side AD will be greater than AB.

Lastly for problem 11, "AB = BC; AD ≅ CD," option C aligns since if two pairs of sides are equal in length respectively then their opposite angles will also be congruent due to the properties of a parallelogram.

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