Question

PLSS help me with this question?

Answer 1

Answer:

Part a) By alternate interior angles

Part b) By vertical angles

Part c)  By AAA (Angle-Angle-Angle) Similarity Theorem

Part d) Triangles ABC and CDE are similar

Part e) $b=\frac{2DE}{3}$  or  $b=\frac{15}{AC}$

Step-by-step explanation:  

Part a)

we know that

If AB is parallel to DE

then

m<1=m<4 ------> by alternate interior angles

Part b)

we know that

m<5=m<6 -------> by vertical angles

Part c) we know that

The two triangles are similar by AAA (Angle-Angle-Angle) Similarity Theorem ------> The three corresponding angles are equal

so

m<1=m<4

m<5=m<6

m<3=m<2

Part d) we know that

If two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

therefore

Triangles ABC and CDE are similar

Part e) Find the length side of b

Remember that

If two figures are similar, then the ratio of its corresponding sides is equal

so

$\frac{AB}{DE}=\frac{BC}{DC}=\frac{AC}{CE}$

substitute the values

$\frac{3}{DE}=\frac{2}{b}=\frac{AC}{7.5}$  

$b=\frac{2DE}{3}$

or

$b=\frac{2*7.5}{AC}=\frac{15}{AC}$