Question 9(Multiple Choice Worth 6 points)(05.01 LC)The figure below shows triangle NRM with r2 = m2 + n2:Triangle NRM has legs m and n, and r is the length of its longest side.Ben constructed a right triangle EFD with legs m and n, as shown below:Triangle EFD has legs m and n and hypotenuse f.He made the following table to prove that triangle NRM is a right triangle:Statement Reason1. r2 = m2 + n2 Given2. f2 = m2 + n2 Pythagorean Theorem3. f2 = r2 Substitution4. f = r Square Root Property of Equality5. Triangle NRM is congruent to triangle EFD SSS Postulate6. Angle NRM is a right angle ?7. Triangle NRM is a right triangle Angle NRM is a right angleWhich reason best fits statement 6? Triangle Proportionality Theorem All sides of both the triangles are equal Corresponding parts of congruent triangles are congruent Triangle EFD has two angles which measure less than 90°
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Answer: Corresponding parts of congruent triangles are congruent.Step-by-step explanation:When two triangles are congruent then their corresponding parts of are also congruent.In the given proof, Statement 5 says Δ NRM≅ Δ EFD which provides that ∠NRM=∠EFD=90 ° because of the property that corresponding parts of congruent triangles are congruent.Therefore, Corresponding parts of congruent triangles are congruent. best fits statement 6.
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