Question

Given that the two triangles are similar, answer the following questions.

(a) Write the similarity statement.

(b) List all of the equal angles.

(c) Write the extended proportion for the side lengths.

(d) If AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589, solve for x.

Answer 1

Question (a)

Triangle AUV is similar to triangle ABC

Question (b)

Angle U = Angle B
Angle V = Angle C

Question (c)

Side AU corresponds to side AB
Side AV corresponds to side AC
Side UV correspond to side BC

Question (d)

$\frac{AV}{AC}= \frac{20x+108}{20x+108+273}$
$\frac{372}{589}= \frac{20x+108}{20x+381}$
$372[20x+381]=589[20x+108]$
$7440x+141732=11780x+63612$
$141732-63612=11780x-7440x$
$78120=4340x$
$x= \frac{78120}{4340}=18$