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Geometry Problem: Finding EC in Triangle ABC
The problem involves a triangle ABC where a line segment DE is drawn parallel to BC, intersecting sides AB and AC at points D and E, respectively. We are given the lengths AD = 3, DB = 6, and AE = 4, and we need to find the length of EC.
Applying the Basic Proportionality Theorem
When a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides the two sides proportionally. This is known as the Basic Proportionality Theorem (BPT) or Thales's Theorem.
According to the BPT, for triangle ABC with DE || BC:
$ \frac{AD}{DB} = \frac{AE}{EC} $
Calculation Step-by-Step
- Substitute Given Values: Plug the known lengths into the BPT formula:
$ \frac{3}{6} = \frac{4}{EC} $
- Simplify the Ratio: Simplify the fraction on the left side:
$ \frac{1}{2} = \frac{4}{EC} $
- Solve for EC: Cross-multiply to find the value of EC:
$ 1 \times EC = 2 \times 4 $
$ EC = 8 $
Therefore, the length of EC is 8.
Similar Questions
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Important Questions from Triangles, Congruence and Similarity
Angle between the internal bisectors of two angles ∠B and ∠C of a ΔABC is 132°, then the value of ∠A is
In ΔPQR, PQ = PR and S is a point on QR such that ∠PSQ = 96° + ∠QPS and ∠QPR = 132°. What is the measure of ∠PSR?
In Δ ABC, ∠A = 50°. If the bisectors of the angle B and angle C, meet at a point O, then ∠BOC is equal to:
Triangle ABC is right angled at B. BD is an altitude intersecting AC at D. If AC = 9 cm and CD = 3 cm. then find the measure of AB (in cm).
The base and altitude of an isosceles triangle are 10 cm and 12 cm respectively. Then the length of each equal side is:
