Question

ΔABC and ΔDEF are similar. The lengths of AB  and AC are 5 units each, and the length of BC  is 6 units.If the length of EF  is 3 units, then the length of DE  is units.?If m

Answer 1

Step-by-step explanation

First, let us make a sketch of the triangles:

The two triangles are similar. This implies that the ratios of the corresponding sides of the triangles are equal in length. Also, the corresponding angles are equal in measure.

To find the length of DE, we have to apply the ratios of the corresponding lengths of the triangles:

`(AB)/(BC)=(DE)/(EF)`

Substitute the given values and solve for DE:

`\begin{gathered} (5)/(6)=(DE)/(3) \\ \\ DE=(3*5)/(6) \\ \\ DE=2.5\text{ units} \end{gathered}`

That is the length of DE.

The two given triangles are isosceles triangles. This is because the two sides of triangles ABC and are equal in length.

In an isosceles triangle, the angles at the base are equal in measure. This, therefore, implies that for triangle ABC: