1. ## triangles

hi i need to have a PERFECT SOLUTION by tomorrow for this...and i have NO idea how to do it...im really FREAKING out....please help me!!!

MO = 5cm
OP = (y+1)cm
OQ = (2y-2)cm
NO = 4cm

i) show that triangles MNO and QPO are similar.
ii) explain why (2y-2)/5=(y+1)/4
iii)solve the equation in (ii)

2. Originally Posted by mrmann
hi i need to have a PERFECT SOLUTION by tomorrow for this...and i have NO idea how to do it...im really FREAKIG out....please help me!!!

MO = 5cm
OP = (y+1)cm
OQ = (2y-2)cm
NO = 4cm

i) show that triangles MNO and QPO are similar.
ii) explain why (2y-2)/5=(y+1)/4
iii)solve the equation in (ii)
Hi mrmann,

i) The two triangles are similar because of the AA postulate which says "If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar"

Angle M is congruent to angle Q and angle N is congruent to angle P because they are alternate interior angles between the two parallel lines.

ii) Explain why $\displaystyle \frac{2y-2}{5}=\frac{y+1}{4}$

When two triangles are similar, their corresponding sides are proportional.

iii) Solve $\displaystyle \frac{2y-2}{5}=\frac{y+1}{4}$

$\displaystyle 4(2y-2)=5(y+1)$

$\displaystyle 8y-8=5y+5$

$\displaystyle 3y=13$

$\displaystyle y=\frac{13}{3}$