If triangles ABC and MPK are similar, with AB: MP = BC: PK, angle B = angle P, then

If triangles ABC and MPK are similar, with AB: MP = BC: PK, angle B = angle P, then: 1) AC: PK = BC: MK 2) AB: PM = AC: MP 3) AB: MP = MP: AC 4) BC: PK = AC: PM

Let us write down the formulas for the similarity of these triangles: AB: MP = BC: RK, whence: AB * PK = MP * BC; (1)

1) AC: PK = BC: MK, we write down the consequence: AC * MK = PK * BC – prove. AC: MK = BC: PK, or AC * PK = MK * BC (2), we divide (1) by (2) we get: AB: AC = MP: MK – this is true for similar triangles.

2) AB: PI = AC: MP; AB: AC = PM: MP = 1, but this is not always true.

3) AB: MP = MP: AC; AB * AC = MP * MP eo does not follow from the similarity.

4) BC: PK = AC: PM; ВС: АС = РК: РМ is also a formula of non-corresponding parties, and it is not always true.