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Answer:
See explanation
Step-by-step explanation:
<u>Given:</u> ΔABC ≅ ΔDEF
AM, DN - medians
<u>Prove:</u> AM ≅ DN
Proof:
1. Congruent triangles ABC and DEF have congruent corresponding parts:
- AB ≅ DE;
- BC ≅ EF;
- ∠ABC ≅ ∠DEF.
2. BM ≅ MC - definition of the median AM;
3. EN ≅ NF - definition of the median DN;
4. AB ≅ 2BM, EF ≅ 2EN
BM ≅ 1/2 AB,
EN ≅ 1/2 EF,
thus, BM ≅ EN
5. Consider two triangles ABM and DEN. In these triangles \:
- AB ≅ DE (see 1));
- BM ≅ EN (see 4));
- ∠ABM ≅ ∠DEN (see 1).
So, ΔABM ≅ ΔDEN by SAS postulate.
6. Congruent triangles ABM and DEN have congruent corresponding sides BM and DN.
