The Correct Answer and Explanation is:
Of course. Here are the correct answers for the worksheet, followed by a detailed explanation.
Correct Answers
- AC ≅ DF
- AB ≅ DE
- BC ≅ EF
- ∠A ≅ ∠D
- ∠D ≅ ∠A
- ∠B ≅ ∠E
- △CBL ≅ △FED (assuming CBL is a typo for CBA)
- △DFE ≅ △ACB
- △BAC ≅ △EDF
- △EDF ≅ △BAC
Explanation
The key to solving this worksheet lies in understanding the initial congruence statement: △ABC ≅ △DEF. This single line provides all the information needed to determine how the two triangles correspond to each other. In geometry, the order of the letters in a congruence statement is critical because it tells you exactly which vertices, angles, and sides match up.
From △ABC ≅ △DEF, we can establish the following correspondence:
- The first vertex, A, corresponds to the first vertex, D.
- The second vertex, B, corresponds to the second vertex, E.
- The third vertex, C, corresponds to the third vertex, F.
This principle is often called “Corresponding Parts of Congruent Triangles are Congruent” (CPCTC).
Solving for Sides and Angles (Questions 1-6):
We apply this correspondence to find the congruent parts.
- For the sides: The side connecting vertices A and C (AC) must be congruent to the side connecting the corresponding vertices D and F (DF). Similarly, side AB corresponds to DE, and side BC corresponds to EF.
- For the angles: The angle at vertex A (∠A) must be congruent to the angle at the corresponding vertex D (∠D). Likewise, ∠B is congruent to ∠E, and ∠C is congruent to ∠F.
Solving for Triangle Congruence (Questions 7-10):
The same logic extends to naming the entire triangle. The order of vertices must match the established correspondence.
- For question 9, △BAC, we look at the corresponding vertices in order: B corresponds to E, A corresponds to D, and C corresponds to F. Therefore, △BAC is congruent to △EDF.
- For question 8, △DFE, we find the matches: D corresponds to A, F corresponds to C, and E corresponds to B. This means △DFE is congruent to △ACB.
- Question 7 contains a likely typographical error, listing a point “L” that does not exist. Assuming it meant to be △CBA, the corresponding vertices are F, E, and D, making it congruent to △FED.
