This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Question 45: The question asks which of the given conditions is not a sufficient condition for two triangles to be congruent. A. AAS (Angle-Angle-Side): This is a valid congruence criterion. If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent. B. SSS (Side-Side-Side): This is a valid congruence criterion. If three sides of one triangle are equal to three corresponding sides of another triangle, the triangles are congruent. C. SAS (Side-Angle-Side): This is a valid congruence criterion. If two sides and the included angle of one triangle are equal to two corresponding sides and the included angle of another triangle, the triangles are congruent. D. SSA (Side-Side-Angle): This is not* a valid congruence criterion. If two sides and a non-included angle of one triangle are equal to two corresponding sides and a non-included angle of another triangle, the triangles are not necessarily congruent. This is known as the ambiguous case. The final answer is D. SSA. Question 46: A woman received a 20% discount on a piece of cloth and paid 525.00. We need to find the original price. Step 1: Determine the percentage of the original price paid. If there is a 20% discount, the woman paid 100\% - 20\% = 80\% of the original price. Step 2: Set up an equation. Let P be the original price. 0.80 × P = \525.00 Step 3: Solve for P. P = (\525.00)/(0.80) P = \656.25 The final answer is C. \656.25$.