TACHS Quiz: Selecting By Classification Rule
18 questions · exam conditions
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Selecting By Classification RuleQuestion 1 of 18

Isosceles triangle, arrow, kite. Which also belongs?

Regular pentagon (5 axes)
Isosceles trapezoid (1 axis)
Scalene triangle (no axes)
Circle (infinite axes)
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TACHS Quiz

TACHS Quiz: Selecting By Classification Rule

Practice Selecting By Classification Rule 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 Selecting By Classification Rule, 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

Isosceles triangle, arrow, kite. Which also belongs?

  1. Regular pentagon (5 axes)
  2. Isosceles trapezoid (1 axis) (correct answer)
  3. Scalene triangle (no axes)
  4. Circle (infinite axes)
Explanation: Each shape in the set has exactly one line of symmetry: an isosceles triangle, an arrow, and a kite all fold in half one way. An isosceles trapezoid also has one axis of symmetry, so it belongs. The regular pentagon tempts because it is symmetrical, but it has 5 axes, not one; a circle has infinite and a scalene triangle has none.

Question 2

Set: 3-4-5, 6-8-10, 9-12-15 triangles. Which also belongs?

  1. 12-16-20 right triangle (correct answer)
  2. 5-12-13 right triangle
  3. 2-3-4 scalene triangle
  4. Isosceles right triangle
Explanation: Each listed triangle is a 3-4-5 right triangle scaled by 1, 2, and 3. The next in that pattern is 12-16-20, scaled by 4, and it is a right triangle because 12^2 + 16^2 = 144 + 256 = 400 = 20^2. The tempting 5-12-13 is also a right triangle, but it is a different Pythagorean triple, not part of the 3-4-5 family.

Question 3

2 squares share a side; 2 equilateral triangles share a side; 2 regular hexagons share a side. Which also belongs?

  1. 2 non-square rectangles joined
  2. 2 circles touch at a point
  3. Square and triangle share side
  4. 2 regular octagons share side (correct answer)
Explanation: Each pair listed is two congruent regular polygons joined along a side. Two regular octagons sharing a side fit that exactly. The tempting trap is two non-square rectangles joined: they share a side, but a non-square rectangle is not a regular polygon because its sides are not all equal.

Question 4

Set: rhombus, kite, isosceles trapezoid. Which also belongs?

  1. Non-square rectangle (correct answer)
  2. Slanted parallelogram
  3. Scalene quadrilateral
  4. Right trapezoid shape
Explanation: Rhombus, kite, and isosceles trapezoid all have at least one line of reflection symmetry. A non-square rectangle also has two such symmetry lines, so it belongs. The tempting slanted parallelogram is wrong because, while it is a parallelogram like the rhombus, its generic form has no line of symmetry.

Question 5

Slanted parallelogram, letter Z, pinwheel. Which also belongs?

  1. Uppercase H (2 axes)
  2. Regular hexagon (6 axes)
  3. Uppercase S (rotational) (correct answer)
  4. Isosceles triangle (1 axis)
Explanation: The three examples all have rotational symmetry but no line of reflection: a slanted parallelogram, Z, and a pinwheel each rotate onto themselves but can't be mirrored onto themselves. Uppercase S also has only 180-degree rotational symmetry, so it fits. Uppercase H is tempting because it has point symmetry, but its vertical and horizontal reflection axes break the pattern.

Question 6

The three figures on the left are classified together. Which figure on the right fits this classification?

  1. A 5-pointed star with 1 point shaded
  2. A 6-pointed star with 3 alternating points shaded (correct answer)
  3. A 4-pointed star with 2 adjacent points shaded
  4. A 7-pointed star with 3 points shaded
Explanation: Each given figure is a star with an EVEN number of points where exactly HALF of the points are shaded in an alternating pattern. Figure 1: 4-point star, 2 alternating points shaded. Figure 2: 6-point star, 3 alternating shaded. Figure 3: 8-point star, 4 alternating shaded. Choice B (6 points, 3 alternating) fits. Choice A has 5 points (odd). Choice C has 2 ADJACENT shaded points (not alternating). Choice D has 7 points (odd) and is not half-shaded.

Question 7

Refer to the figure below. The three scatter plots in the Set display a certain correlation. Which answer plot displays the same correlation?

  1. Figure A (correct answer)
  2. Figure B
  3. Figure C
  4. Figure D
Explanation: All Set plots show a strong negative linear correlation (points fall roughly on a downward-sloping line). Answer plot A also shows a strong negative linear trend. Plot B shows no correlation, C positive correlation, D curved (quadratic) pattern.

Question 8

The three figures on the left follow a rule. Which figure on the right follows the same rule?

  1. A shape with 2 curved sides and 2 straight sides (correct answer)
  2. A shape with 3 curved sides and 0 straight sides
  3. A shape with 0 curved sides and 4 straight sides
  4. A shape with 1 curved side and 3 straight sides
Explanation: Each given shape has an EQUAL number of curved sides and straight sides. Figure 1: 1 curved, 1 straight (semicircle). Figure 2: 2 curved, 2 straight. Figure 3: 3 curved, 3 straight. Choice A has 2 curved and 2 straight — equal. Choice B has 3 curved, 0 straight (not equal). Choice C has all straight sides. Choice D has 1 curved, 3 straight (not equal). Students focused on 'must have curves' may pick B; those focused on counting sides to a certain number may pick D.

Question 9

Look at the three figures on the left. Find the answer choice that belongs with them.

  1. A circle with 4 tick marks around it evenly spaced
  2. A circle with 5 tick marks around it evenly spaced
  3. A circle with 6 tick marks unevenly spaced
  4. A circle with 7 tick marks evenly spaced (correct answer)
Explanation: Each given figure is a circle with a PRIME number of evenly-spaced tick marks around its circumference: 2, 3, and 5 ticks. Choice D has 7 ticks (prime) evenly spaced. Choice A has 4 ticks (not prime). Choice B has 5 ticks (prime) but this duplicates figure 3 on the left — a strong student knows the answer should not be identical to a given figure, and additionally re-reading: the rule is prime AND not already shown, so 7 is the next prime. Choice C has uneven spacing, violating the rule. Many students will pick B thinking 'prime number' is enough.

Question 10

Look at the three figures on the left. Find the figure on the right that belongs to the same group.

  1. A circle divided into 4 equal parts, 1 shaded
  2. A circle divided into 6 equal parts, 2 shaded (correct answer)
  3. A circle divided into 5 equal parts, 2 shaded
  4. A circle divided into 8 equal parts, 3 shaded
Explanation: Each given circle is divided into parts with exactly one-third of the parts shaded. Figure 1: 3 parts, 1 shaded (1/3). Figure 2: 6 parts, 2 shaded (1/3). Figure 3: 9 parts, 3 shaded (1/3). Choice B (2/6 = 1/3) follows the rule. Choice A (1/4) is a trap — students may think '1 shaded' is the rule. Choice C (2/5) and Choice D (3/8) are close to 1/3 but not equal.

Question 11

The figures on the left share a common feature. Which figure on the right fits with them?

  1. A shape with 3 lines of symmetry
  2. A shape with exactly 1 line of symmetry (correct answer)
  3. A shape with 0 lines of symmetry
  4. A shape with exactly 2 lines of symmetry
Explanation: Each of the three given figures has exactly ONE line of symmetry (an isosceles trapezoid, a heart shape, and an arrow — each has a single vertical axis of symmetry). Choice B has exactly one line of symmetry. Choice A (equilateral triangle) has three lines of symmetry. Choice C (scalene shape) has none. Choice D (rectangle) has two lines of symmetry. Students who focus on 'the shapes look symmetric' without counting axes may pick A or D.

Question 12

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

  1. A pentagon with a small black triangle inside touching one side
  2. A hexagon with a small black circle inside touching one side (correct answer)
  3. A square with a small black circle in the exact center
  4. A triangle with a small white circle inside touching one side
Explanation: The three given figures each show a polygon with an EVEN number of sides containing a small black shape that touches one side of the polygon. Choice B (hexagon, 6 sides, with a black circle touching a side) matches all three rules. Choice A fails because a pentagon has an odd number of sides. Choice C fails because the inner shape does not touch a side — it is centered. Choice D fails because the polygon has an odd number of sides AND the inner shape is white, not black.

Question 13

The three figures on the left go together in some way. Which figure on the right belongs with them?

  1. A figure with 4 dots and 2 lines
  2. A figure with 5 dots and 3 lines
  3. A figure with 6 dots and 3 lines (correct answer)
  4. A figure with 4 dots and 3 lines
Explanation: In each of the three given figures, the number of dots is exactly twice the number of line segments. Figure 1: 4 dots, 2 lines (4=2×2). Figure 2: 8 dots, 4 lines. Figure 3: 10 dots, 5 lines. Choice C with 6 dots and 3 lines satisfies 6=2×3. Choice A appears to match the first given figure exactly, which is a trap — classification answers should not simply duplicate a given figure. Choices B and D have ratios that are not 2:1.

Question 14

The three figures on the left all follow one rule. Pick the figure on the right that follows the same rule.

  1. A white square containing a black square containing a white circle
  2. A black triangle containing a white triangle containing a black triangle
  3. A white circle containing a black circle containing a white triangle
  4. A black circle containing a white square containing a black circle (correct answer)
Explanation: Each given figure contains three nested shapes where (1) the colors alternate black–white–black from outside in, and (2) the outermost and innermost shapes are the SAME type of shape, while the middle shape is different. Choice D: black circle, white square, black circle — colors alternate black-white-black, and outer/inner are both circles. Choice A has colors white-black-white (wrong order) and three different shapes. Choice B has all three shapes the same type (all triangles). Choice C has colors white-black-white (wrong starting color).

Question 15

Study the figures on the left. Pick the figure on the right that matches their pattern.

  1. A rectangle with arrows on opposite short sides pointing inward
  2. A rectangle with arrows on opposite long sides pointing outward (correct answer)
  3. A rectangle with arrows on adjacent sides pointing inward
  4. A rectangle with arrows on all four sides pointing outward
Explanation: In each given figure, the arrows are on OPPOSITE sides of the shape and point in OPPOSITE directions AWAY from the center (outward). Figure 1: arrows on top and bottom pointing up and down. Figure 2: arrows on left and right pointing left and right. Figure 3: arrows on opposite sides of a hexagon pointing outward. Choice B matches both rules. Choice A has arrows on opposite sides but pointing INWARD. Choice C has arrows on ADJACENT sides, not opposite. Choice D has arrows on all four sides, not just two.

Question 16

Study the three figures on the left. Choose the figure on the right that follows the same rule.

  1. A circle with a vertical arrow inside pointing up
  2. A triangle with a diagonal arrow inside pointing up-right
  3. A square with a horizontal arrow inside pointing left
  4. A pentagon with a diagonal arrow inside pointing down-left (correct answer)
Explanation: In each given figure, the arrow inside points toward a VERTEX (corner) of the enclosing shape, not toward a side. Figure 1: triangle with arrow pointing to top vertex. Figure 2: square with arrow pointing to top-right corner. Figure 3: hexagon with arrow pointing toward one of its vertices. Choice D's pentagon has the arrow pointing toward a vertex. Choice A is wrong because a circle has no vertices. Choice B's arrow points at a side, not a vertex. Choice C's arrow points at the middle of the left side, not a corner.

Question 17

Examine the three figures on the left. Which figure on the right belongs with them?

  1. Two parallel horizontal lines with 2 dots between them
  2. Two parallel vertical lines with 4 dots between them
  3. Two parallel diagonal lines with 3 dots between them (correct answer)
  4. Two crossing lines with 3 dots between them
Explanation: In each given figure, there are exactly two parallel lines with a number of dots equal to the number of line-endpoints showing (each line has 2 endpoints, but the rule is that the dots between them equal ONE MORE than in the previous figure: 1, 2, 3... wait — the consistent rule is: two PARALLEL lines with an ODD number of dots between them. Figure 1: 1 dot. Figure 2: 3 dots. Figure 3: 5 dots. Choice C has two parallel diagonal lines with 3 dots (odd) between them. Choice A has 2 dots (even). Choice B has 4 dots (even). Choice D fails because the lines cross (not parallel).

Question 18

The three figures on the left share a property. Pick the figure on the right with that same property.

  1. A rectangle divided into 4 equal strips, with strips 2 and 4 shaded
  2. A rectangle divided into 5 equal strips, with strips 2 and 4 shaded
  3. A rectangle divided into 4 equal strips, with strips 1 and 2 shaded
  4. A rectangle divided into 6 equal strips, with strips 1, 3, and 5 shaded (correct answer)
Explanation: In each given figure, the rectangle is divided into an EVEN number of equal strips, and the shaded strips are in ODD positions (1st, 3rd, 5th...) — meaning shaded and unshaded alternate starting with shaded. Figure 1: 2 strips, strip 1 shaded. Figure 2: 4 strips, strips 1 and 3 shaded. Figure 3: 8 strips, strips 1, 3, 5, 7 shaded. Choice D has 6 strips with strips 1, 3, 5 shaded — matches the pattern. Choice A has even positions shaded (not odd). Choice B has an ODD number of strips (5). Choice C has adjacent strips shaded (not alternating).