If a, B, C are the three sides of triangle ABC, and a (a-b) + B (B-C) + C (C-A) = 0, try to judge the shape of triangle ABC and explain the reason

If a, B, C are the three sides of triangle ABC, and a (a-b) + B (B-C) + C (C-A) = 0, try to judge the shape of triangle ABC and explain the reason

a(a-b)+b(b-c)+c(c-a)=0a²-ab+b²-bc+c²-ca=02a²-2ab+2b²-2bc+2c²-2ca=0a²-2ab+b²+b²-2bc+c²+c²-2ac+a²=0（a-b）²+（b-c）²+（c-a）²=0...

In triangle ABC, if 3 ∠ a = 3 / 2 ∠ B = C, try to judge the shape of △ ABC and explain the reason

ABC is a right triangle
reason:
∵3∠A=3/2 ∠B=∠C
∴∠B=2∠A     ∠C=3∠A
∵∠A+∠B+∠C=180°
∴∠A+2∠A+3∠A=180°
    6∠A=180°
∴∠A=30°
∴∠C=3∠A=90°
The ABC is a right triangle

In △ ABC, ∠ ACB = 90 °, M is the midpoint of BC, CN ⊥ am, and the perpendicular foot is n. AB / am = BN / BM is proved
Need in time

To prove AB / am = BN / BM, that is to say, △ AMB and △ BMN are similar;
The similarity of these two triangles can be proved by ∠ AMB = ∠ BMN and am / BM = BM / Mn;
Because m is the middle point, am / BM = BM / Mn, that is am / cm = cm / Mn, am / cm = cm / Mn can be obtained by proving that two right triangles are similar, or directly applying the formula