In triangle ABC, DE is parallel to BC. If AD = 1.5 cm, DB = 3 cm and AE = 1 cm, find EC.

Step 1: Identify Similar Triangles

Given that DE is parallel to BC, we can conclude that triangle ADE is similar to triangle ABC. This is because corresponding angles are equal (angle D = angle B, angle E = angle C, and angle A is common). This is known as the AA similarity criterion.

Step 2: Apply Basic Proportionality Theorem

According to the Basic Proportionality Theorem (also known as Thales Theorem or the Intercept Theorem), if a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

Step 3: Substitute Known Values

We are given $AD = 1.5$ cm, $DB = 3$ cm, and $AE = 1$ cm. Substitute these values into the proportionality equation.

Step 4: Solve for EC

Now, we solve the equation for EC. Cross-multiply the terms and then isolate EC to find its value.

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