Introduction
Embedded Figures is a non-verbal reasoning topic in SSC CGL Tier-I. A complex figure contains a simpler figure hidden within it. You must identify which of the given simple figures is embedded in the complex figure. This tests observation, visualisation, and pattern recognition.
Understanding Embedded Figures
In embedded figures problems, a complex figure is given, followed by four simple figures. One of the simple figures is hidden inside the complex figure. The hidden figure may be rotated, but its shape and proportions remain the same. You need to mentally separate the overlapping lines to find the embedded figure.
Key Points
- The embedded figure is exactly the same shape as one of the options, possibly rotated.
- Lines of the complex figure may be shared by multiple shapes; focus on the outline of the target figure.
- Eliminate options that have extra lines or missing segments compared to the complex figure.
Solved Example 1
Question: A complex figure shows a large triangle with a horizontal line and a vertical line inside. Which simple figure is embedded? Options: (A) square, (B) smaller triangle, (C) circle, (D) pentagon.
Solution: B
Explanation: The horizontal and vertical lines divide the large triangle into smaller triangles. One of these smaller triangles matches option B exactly. Other options are not present because their shapes do not appear in the complex figure.
Techniques to Solve Embedded Figures
Use a systematic approach: first, scan the complex figure for the overall outline of each option. Then, check if the internal lines of the complex figure can form that outline. Rotate the option mentally if needed. Practice with common shapes like triangles, squares, and quadrilaterals.
Key Points
- Start with the most distinctive feature of each option (e.g., a curved edge or a sharp angle).
- If an option has a curve, look for curves in the complex figure; if none, eliminate it.
- Count the number of sides or vertices; the embedded figure must have the same count.
Solved Example 1
Question: A complex figure consists of a rectangle with two diagonals. Which simple figure is embedded? Options: (A) triangle, (B) circle, (C) hexagon, (D) star.
Solution: A
Explanation: The diagonals divide the rectangle into four triangles. Each triangle is embedded in the complex figure. Options B, C, and D are not present because there are no curves or six-sided shapes.
Practice Questions
Q1. A complex figure shows a square with a diagonal and a line from one corner to the midpoint of the opposite side. Which simple figure is embedded? Options: (A) right triangle, (B) equilateral triangle, (C) circle, (D) trapezium.
Answer: A
Explanation: The diagonal and the line from corner to midpoint create right triangles within the square. An equilateral triangle is not possible because the angles are not 60°. No circle or trapezium is formed.
Q2. A complex figure is a circle with two perpendicular diameters. Which simple figure is embedded? Options: (A) square, (B) semicircle, (C) quarter circle, (D) rectangle.
Answer: C
Explanation: The two perpendicular diameters divide the circle into four quarter circles. Each quarter circle is embedded. Semicircles are also present but quarter circle is a more precise match if that is an option. However, if both are options, check the exact shape; typically quarter circle is the intended answer for this configuration.
Q3. A complex figure shows a large triangle with a smaller inverted triangle inside, sharing the same base. Which simple figure is embedded? Options: (A) parallelogram, (B) rhombus, (C) trapezium, (D) kite.
Answer: C
Explanation: The region between the large triangle and the inverted triangle forms three smaller triangles, but the overall shape of the large triangle minus the inverted triangle is not a single simple figure. However, if the inverted triangle is placed such that its top vertex touches the midpoint of the base, the remaining shape includes trapeziums. Specifically, the shape formed by the top part of the large triangle and the inverted triangle's sides creates a trapezium. Thus, a trapezium is embedded.
Common Mistakes
- Assuming the embedded figure must be in the same orientation as the option; it can be rotated.
- Overlooking that the embedded figure may share lines with other parts of the complex figure.
- Choosing an option that has an extra line or missing segment compared to the complex figure.
Quick Revision
- Embedded figures are hidden within a complex figure, possibly rotated.
- Use elimination: check for curves, number of sides, and distinctive features.
- Practice with common shapes: triangles, quadrilaterals, circles, and their parts.