Answer:
A. ∆ABD ~ ∆CDE
B. x ≈ 5.3
Step-by-step explanation:
A. The Acute Angle Similarity Theorem states that when an acute angle in one right triangle is congruent to a corresponding acute angle in another, both right triangles are said to be similar to each other.
<B ≅ <D (both are right angles)
<A ≅ C,
Therefore, ∆ABD ~ ∆CDE
B. Since ∆ABD ~ ∆CDE, corresponding sides would be proportional to each other. This means that:
DE/BD = CD/AB
Substitute:
6/8 = 4/x
Cross multiply
6*x = 4*8
6x = 32
6x/6 = 32/6
x ≈ 5.3 (nearest tenth)
