Core ConceptRead this first — the foundation of the topic
Let's work through an example
Simple Figure: A right triangle with one horizontal line and one vertical line forming a 90-degree angle
Complex Figure Options
1
Identify the key features of the simple figure - right angle, horizontal base, vertical height.
2
Look for the same right angle pattern in each complex figure. Eliminate figures that don't have this exact angle combination.
3
Trace the complete triangle shape within the remaining options. Check if all three sides can be found without breaks or distortions.
4
Verify that the proportions match the original figure. In this case, the correct answer would be the complex figure where you can trace the complete right triangle maintaining its exact shape and proportional relationships. Another effective trick is the 'Elimination Method' - quickly eliminate options that clearly don't contain enough lines or shapes to form the required figure. If the simple figure has 5 distinct line segments, the complex figure must have at least 5 line segments in the correct arrangement.
Exam TrapsCommon mistakes students make — avoid these
include accepting distorted versions of the target figure or missing rotated orientations. Students often get confused when the embedded figure appears upside down or sideways. Remember, rotation is allowed but shape distortion is not.
Practice identifying figures in different orientations to build this skill. The key to mastering embedded figures is systematic scanning and pattern recognition rather than random searching.
Key Points to Remember
Embedded figure maintains exact shape and size but can be rotated or flipped
Simple figure cannot be stretched, distorted, or have proportions changed
Use Corner Method - identify unique angles and corners first for quick elimination
Systematic scanning beats random searching every time
Complex figure must contain at least the same number of line segments as simple figure
Rotation in any direction (90°, 180°, 270°) is perfectly acceptable
In a complex figure, a large hexagon contains three overlapping shapes: a square overlapping with a circle, and both overlapping with a triangle. The overlapping region of the square and circle contains a small dot. Which of the following best describes what is embedded in the figure?
(a) Only the square and circle overlap; the triangle is separate
(b) All three shapes (square, circle, triangle) overlap in some region
(c) The square and triangle overlap, but the circle is separate
(d) Only the circle and triangle overlap; the square is separate
Practice 2easy
A figure shows a large rectangle with a diagonal line dividing it into two triangles. The upper triangle contains a small circle and a small square. The lower triangle contains a small rectangle and a small pentagon. If we remove the diagonal line, which shapes remain embedded in the figure?
(a) Circle, Square, Rectangle, Pentagon
(b) Circle, Square only
(c) Rectangle, Pentagon only
(d) Circle, Rectangle only
Practice 3medium
A composite figure shows a large square subdivided into 9 equal smaller squares (3×3 grid). The center square contains a small diamond. The 4 corner squares each contain a small triangle. The 4 edge-middle squares are empty. An embedded pattern is defined as: the center square plus any 2 of the 4 corner squares that are diagonally opposite to each other. How many such embedded patterns exist?
Practice 4medium
A figure shows a hexagon with 6 vertices labeled A, B, C, D, E, F in clockwise order. Inside the hexagon, there are 3 non-overlapping triangles: Triangle 1 connects vertices A-B-C, Triangle 2 connects vertices C-D-E, and Triangle 3 connects vertices E-F-A. An embedded pattern is defined as any single triangle that shares exactly 2 vertices with the hexagon's perimeter. How many embedded patterns of this type exist in the figure?
Practice 5medium
A figure consists of a large circle with 4 smaller circles positioned at North, South, East, and West points on its circumference. Inside the large circle, there is a cross (+ shape) formed by one vertical and one horizontal line passing through the center. An embedded figure is defined as: one of the 4 smaller circles PLUS the portion of the cross that lies within that circle's boundary. How many distinct embedded figures of this type can be identified?
Practice 6medium
A rectangular grid contains 12 small squares arranged in 3 rows and 4 columns. Some squares are shaded black, others are white. An embedded pattern is defined as any 2×2 sub-grid (4 adjacent squares in a square formation) where exactly 3 squares are black and 1 is white. How many such embedded patterns exist in a grid where the first two rows are entirely black and the third row is entirely white?
Practice 7medium
A complex star-shaped figure is composed of a central pentagon surrounded by 5 triangular points. Within this figure, a smaller embedded pattern consists of the central pentagon plus exactly 2 adjacent triangular points (sharing edges with the pentagon). How many different ways can this embedded pattern be extracted from the main figure?
Practice 8hard
A figure shows a large circle divided into 8 equal sectors by 4 diameters (creating 8 pie-shaped regions). A rectangle is embedded such that its four corners touch four different sectors, with two opposite corners on the circle's circumference and two opposite corners inside the circle. The rectangle is oriented such that its sides are not parallel to any diameter. How many of the 8 sectors does the embedded rectangle occupy (completely or partially)?
Practice 9hard
A complex figure contains a large square with two diagonal lines drawn from opposite corners, creating 4 triangular regions. A circle is inscribed in one of these triangular regions. Additionally, a small parallelogram is embedded such that two of its sides lie along two different edges of the square (not on the diagonals). Which of the following statements about the embedded parallelogram is correct?
Practice 10hard
A figure shows a large hexagon subdivided into 6 equilateral triangles. Inside this hexagon, a smaller irregular quadrilateral is embedded with one vertex touching the center point and the other three vertices touching three non-adjacent triangle edges. How many of the 6 triangular sections does the embedded quadrilateral completely or partially occupy?
Practice 11hard
A figure displays a large rectangle divided by one vertical and one horizontal line through its center, creating 4 equal quadrants. A star shape (5-pointed) is embedded such that its center coincides with the rectangle's center, but it is rotated 36° clockwise from the standard upright position. A small triangle is placed with its base on the top edge of the rectangle and its apex pointing downward into the rectangle. How many of the star's 5 points extend into the top-right quadrant?
Practice 12hard
A complex figure contains a large equilateral triangle subdivided into 9 smaller congruent equilateral triangles (3 rows: 1 on top, 2 in middle, 3 on bottom, with some inverted). A small square is embedded with one vertex at the center of the large triangle and its four sides making 45° angles with the sides of the large triangle. How many of the 9 smaller triangles does the embedded square occupy (completely or partially)?
60-Second Revision — Embedded Figures
Remember: Shape and proportions must remain exactly the same
Technique: Use Corner Method to identify unique angles first
Strategy: Eliminate options with insufficient line segments immediately
Alert: Check all four orientations (0°, 90°, 180°, 270°) systematically
Trap: Don't accept distorted or stretched versions of the target figure
Time Management: Maximum 1.5 minutes per question, move on if stuck
Final Check: Trace the complete figure boundary to confirm the answer