TACHS Quiz: Figure Similarity Identification
17 questions · exam conditions
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Figure Similarity IdentificationQuestion 1 of 17

Study the three figures shown. Decide how they are alike, then choose the answer that belongs with them.

Question graphic
A white circle with a black arrow pointing up
A black square with a white arrow pointing left
A white triangle with a black arrow pointing right
A black circle with a white arrow pointing down
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TACHS Quiz

TACHS Quiz: Figure Similarity Identification

Practice Figure Similarity Identification in TACHS with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Figure Similarity Identification, giving you a quick way to practice the rules, question types, and explanations that matter most for TACHS.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Study the three figures shown. Decide how they are alike, then choose the answer that belongs with them.

  1. A white circle with a black arrow pointing up
  2. A black square with a white arrow pointing left
  3. A white triangle with a black arrow pointing right
  4. A black circle with a white arrow pointing down (correct answer)
Explanation: Each figure on the left is a solid black shape containing a white (unfilled) arrow. The arrow's direction and shape vary, but the shape is always black and the arrow is always white. Only choice D has a black shape with a white arrow.

Question 2

The three figures on the left are alike in a certain way. Refer to the figures shown and pick the one that goes with them.

  1. A figure divided into 4 equal parts, 2 shaded
  2. A figure divided into 6 equal parts, 2 shaded
  3. A figure divided into 5 equal parts, 2 shaded (correct answer)
  4. A figure divided into 8 equal parts, 4 shaded
Explanation: In each of the three figures on the left, exactly 2 sections are shaded and the total number of sections is odd (3, 5, 7). Only choice C has an odd number of sections (5) with 2 shaded.

Question 3

Set: rhombus, rectangle, isosceles trapezoid. Which belongs?

  1. regular pentagon, no parallels
  2. parallelogram without symmetry
  3. kite with no parallel sides
  4. square with four right angles (correct answer)
Explanation: Each member has at least one line of symmetry and at least one pair of parallel sides. A square has both, so it is the match. The kite with no parallel sides is tempting because it is symmetric, but it lacks the parallel sides the set requires.

Question 4

Set: star, arrowhead, crescent. Which belongs?

  1. regular hexagon outline
  2. boomerang outline shape (correct answer)
  3. convex pentagon outline
  4. rectangle outline shape
Explanation: Star, arrowhead, and crescent are all concave outlines: each has an inward notch or indentation. The only choice that shares that feature is the boomerang outline. A regular hexagon is tempting because it is also a closed outline, but every interior angle is less than 180 degrees, so it is convex, not concave.

Question 5

Set: right scalene triangle, right trapezoid, L-shaped hexagon. Which belongs?

  1. rectangle with unequal sides
  2. isosceles trapezoid shape
  3. acute scalene triangle shape
  4. 3-4-5 scalene triangle shape (correct answer)
Explanation: The set is shapes with at least one right angle that are not parallelograms. A 3-4-5 scalene triangle is a right scalene triangle, so it belongs. The tempting rectangle with unequal sides also has right angles, but since it is a parallelogram, it doesn't fit the set.

Question 6

Set: semicircle, sector, capsule. Which belongs?

  1. quarter-circle (one arc) (correct answer)
  2. circle with no straight side
  3. oval with no straight side
  4. triangle with no curves
Explanation: Semicircle, sector, and capsule each combine at least one curved arc with at least one straight edge. A quarter-circle sector also has one arc and two straight radii, so it fits. The tempting wrong choice is circle with no straight side, because it is curved but lacks the straight-edge component that the set shares.

Question 7

Set: parallelogram, regular hexagon, letter S. Which belongs?

  1. isosceles trapezoid figure
  2. equilateral triangle figure
  3. capital letter Z figure (correct answer)
  4. capital letter A figure
Explanation: Parallelogram, regular hexagon, and letter S all have rotational symmetry: they look the same after a half-turn. A capital Z also has 180-degree rotational symmetry, so it belongs. The equilateral triangle is tempting because it has symmetry, but its rotational symmetry is 120 degrees, not a half-turn, so it doesn't match the set.

Question 8

Refer to the figure. Which answer choice fits the rule shown by the set?

  1. A. A bar graph with three bars, the middle bar tallest
  2. B. A bar graph with three bars, all the same height
  3. C. A bar graph with three bars increasing steadily left to right (correct answer)
  4. D. A bar graph with three bars decreasing steadily left to right
Explanation: Each sample bar graph shows three bars increasing in height from left to right. Choice C matches. A has the tallest in the middle, B equal heights, and D decreases, so they do not follow the trend.

Question 9

Look carefully at the three figures on the left. Find the way they are alike, then choose the figure that fits.

  1. An arrow rotated 90° clockwise from vertical with a dot on its tail
  2. An arrow pointing in any direction with a dot at its midpoint
  3. An arrow with a dot exactly at its arrowhead tip (correct answer)
  4. An arrow with two dots, one on each end
Explanation: In each of the three figures on the left, a single dot appears at the pointed tip (arrowhead) of the arrow, regardless of the arrow's direction. Only choice C places the dot at the tip.

Question 10

The figures on the left are alike in a certain way. Based on the figures below, choose the one that belongs in the same group.

  1. A figure with 4 dots arranged in a straight line
  2. A figure with 4 dots forming the corners of a square
  3. A figure with 4 dots where 3 are collinear and 1 is off the line (correct answer)
  4. A figure with 4 dots arranged in a zigzag pattern
Explanation: In each of the three figures on the left, there are 4 dots such that exactly 3 of them lie on a single straight line and the 4th dot lies off that line. Only C matches this configuration.

Question 11

Look at the three figures on the left. Figure out how they are alike, then choose the figure that fits the group based on the figures shown.

  1. A shape with a solid black dot in its interior and an X on its boundary
  2. A shape with an X in its interior and a solid black dot on its boundary (correct answer)
  3. A shape with both a solid black dot and an X in its interior
  4. A shape with a solid black dot inside and no X at all
Explanation: Each of the three figures on the left contains an X drawn inside the shape and a single small solid black dot placed on the shape's boundary (edge). Only choice B describes this exact configuration.

Question 12

Examine the three figures on the left. They are alike in a particular way. Based on the figures shown, pick the one that fits with them.

  1. A large circle containing two medium squares
  2. A large square containing one medium triangle and one small triangle
  3. A large triangle containing two medium circles of the same size (correct answer)
  4. A large pentagon containing two small circles and one medium circle
Explanation: Each figure on the left contains exactly two identical inner shapes of the same size and type. Only choice C follows this pattern with two medium circles of equal size inside a triangle.

Question 13

Examine the three figures shown. They share a property. Using the figures shown, choose the figure that belongs.

  1. A large shape containing 3 small identical shapes with 1 of them shaded
  2. A large shape containing 4 small identical shapes with 2 of them shaded
  3. A large shape containing 5 small identical shapes with 2 of them shaded
  4. A large shape containing 4 small identical shapes with 1 of them shaded (correct answer)
Explanation: In each figure on the left, a large outer shape contains several small identical inner shapes, and exactly one of the inner shapes is shaded. The number shaded is always 1, regardless of how many inner shapes there are. Only D has exactly 1 shaded.

Question 14

Study the three figures on the left and decide how they are alike. Then choose the one that fits best.

  1. A shape where the shaded area is on the right half
  2. A shape where the shaded area touches exactly one vertex
  3. A shape where the shaded area is exactly half the total area
  4. A shape where the shaded area is in the center and does not touch any edge (correct answer)
Explanation: In each of the three figures on the left, a smaller shaded region is drawn inside the larger figure without touching any of its edges. Only D describes a shaded area that is interior and doesn't touch any edge.

Question 15

Look at the three figures on the left. They have something in common. Refer to the figures shown to pick the matching figure.

  1. A figure with 2 lines of symmetry
  2. A figure with exactly 1 line of symmetry
  3. A figure with no lines of symmetry (correct answer)
  4. A figure with 4 lines of symmetry
Explanation: Each of the three figures on the left is asymmetrical—none of them has any line of symmetry. The correct match is a figure with no lines of symmetry.

Question 16

The three figures at the left are all alike in a certain way. Refer to the figures shown and choose the one that goes with them.

  1. A shape whose top half is striped and whose bottom half is shaded gray
  2. A shape whose top half is white and whose bottom half is striped
  3. A shape whose top half is shaded gray and whose bottom half is white
  4. A shape whose top half is striped and whose bottom half is white (correct answer)
Explanation: In each figure on the left, the upper half of the shape is filled with diagonal stripes and the lower half is plain white (unfilled). Only choice D matches this top-striped / bottom-white pattern.

Question 17

Look at the three figures on the left. They are alike in a certain way. Find the figure on the right that is most like them in the same way.

  1. A figure with 4 sides and 1 dot inside
  2. A figure with 5 sides and 4 dots inside (correct answer)
  3. A figure with 6 sides and 3 dots inside
  4. A figure with 3 sides and 2 dots inside
Explanation: In each of the three figures on the left, the number of dots inside is one less than the number of sides of the polygon. A 5-sided figure with 4 dots follows this rule.