Question

Explain, with a test, why the two triangles in each figure are similar. Find the

Answer 1

Answer:

x = 3, y = 6

Step-by-step explanation:

In the figure attached,

If ΔADE and ΔABC are similar triangles, their corresponding sides will be in the same ratio.

By this property,

$\frac{AB}{AD}=\frac{AC}{AE}=\frac{BC}{DE}$

$\frac{AB}{AD}=\frac{AC}{AE}$

$\frac{AD+BD}{AD}=\frac{AE+EC}{AE}$

$\frac{3}{2}=\frac{x+1.5}{x}$

3x = 2x + 3

3x - 2x = 3

x = 3

Similarly, $\frac{AB}{AD}=\frac{BC}{DE}$

$\frac{3}{2}=\frac{y}{4}$

y = $\frac{3\times 4}{2}$

y = 6