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Which condition is NOT sufficient for triangle congruence: AAS, SSS, SAS, or SSA?

Mathematics

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2 parts
45

D. SSA\text{D. SSA}

46

\text{C. } \656.25$

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Part 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\boxed{\text{D. SSA}}.

Part 46

\text{C. } \656.25$

A woman received a 20% discount on a piece of cloth and paid $525.00. We need to find the original price.

  1. Determine the percentage of the original price paid.

    If there is a 20% discount, the woman paid 100%−20%=80%100\% - 20\% = 80\% of the original price.

  2. Set up an equation.

    Let PP be the original price. 0.80×P=$525.000.80 \times P = \$525.00

  3. Solve for PP.

    P=$525.000.80P = \frac{\$525.00}{0.80} P=$656.25P = \$656.25

    The final answer is \boxed{\text{C. } \656.25}$.

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