D and E are points on the sides AB and AC respectively of a . If AB = 10.8 cm, AD = 6.3 cm, AC = 9.6cm, and EC = 4 cm. Determine whether or not.[2]△ABCDE∥BC
Question
D and E are points on the sides AB and AC respectively of a triangle. If
- AB = 10.8 cm
- AD = 6.3 cm
- AC = 9.6 cm
- EC = 4 cm
Determine whether or not .
Solution
To determine whether DE is parallel to BC, we need to use the concept of similar triangles.
Triangles are similar if their corresponding sides are proportional.
In triangle ABC, we have sides AB and AC. In triangle ADE, we have sides AD and AE.
We know that AB = 10.8 cm, AD = 6.3 cm, and AC = 9.6 cm.
We also know that AE = AC - EC = 9.6 cm - 4 cm = 5.6 cm.
Now, we can check if AB/AD = AC/AE.
AB/AD = 10.8 cm / 6.3 cm = 1.7142857142857142
AC/AE = 9.6 cm / 5.6 cm = 1.7142857142857142
Since AB/AD = AC/AE, we can conclude that DE is parallel to BC.
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