Question

Stabiliti daca Δ ABC siΔ MNP sunt asemenea in cazurile urmatoare
a)m(∡A)=55°,m(∡B)=60°,m(∡M)=55°,m(∡P)=65°
b)m(∡B)=72°,m(∡C)=56°,m(∡M)=50°,m(∡N)=72°
c)m(∡B)=48°,m(∡M)=90°,m(∡P)=42°,AB supra MN=BC supra NP
d) m(∡A)=81°,m(∡N)=67°,m(∡P)=32°,AB supra MN=AC supra MP

repede ,va rog!!!!

Answer 1

a) m(∡A)=55°,m(∡B)=60°,m(∡M)=55°,m(∡P)=65°⇔m(∡C)=180-(60+55)⇔m(∡C)=65°⇔m(∡N)=180-(55+65)⇔m(∡N)=60°
Deci, la punctul "a)" sunt asemenea.

b) m(∡B)=72°,m(∡C)=56°,m(∡M)=50°,m(∡N)=72°⇔m(∡A)=180-(72+56)⇔m(∡A)=52°⇔m(∡P)= 180-(60+55)⇔m(∡P)=65
Deci, la punctul "b)" nu sunt asemenea.

c) m(∡B)=48°,m(∡M)=90°,m(∡P)=42°,$\frac{AB}{MN}= \frac{BC}{NP}$⇔m(∡N)=180-(90+42)⇔m(∡N)=48°⇒m(∡A)=90°,m(∡C)=42°
Deci, la punctul "c)" sunt asemenea.

d) m(∡A)=81°,m(∡N)=67°,m(∡P)=32°,$\frac{AB}{MN}= \frac{AC}{MP}$⇔m(∡M)=180-(67+32)⇔m(∡M)=81°⇒m(∡B)=67°, m(∡C)=32°
Deci, la punctul "d)" sunt asemenea.