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ddd [48]
3 years ago
14

Sketch and prove the following for the two congruent triangles ∆ABC and ∆DEF.

Mathematics
1 answer:
madreJ [45]3 years ago
3 0

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.

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