Select the answer choice that follows the same classification rule - TACHS Ability

Study the three figures on the left. Choose the figure on the right that follows the same rule.
Answer: A pentagon with a diagonal arrow inside pointing down-left 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.
Study the figures on the left. Pick the figure on the right that matches their pattern.
Answer: A rectangle with arrows on opposite long sides pointing outward 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.
Examine the three figures on the left. Which figure on the right belongs with them?
Answer: Two parallel diagonal lines with 3 dots between them 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).
The three figures on the left all follow one rule. Pick the figure on the right that follows the same rule.
Answer: A black circle containing a white square containing a black circle 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).
Slanted parallelogram, letter Z, pinwheel. Which also belongs?
Answer: Uppercase S (rotational) 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.
The three figures on the left go together in some way. Which figure on the right belongs with them?
Answer: A figure with 6 dots and 3 lines 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.
Set: 3-4-5, 6-8-10, 9-12-15 triangles. Which also belongs?
Answer: 12-16-20 right triangle 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.
Set: rhombus, kite, isosceles trapezoid. Which also belongs?
Answer: Non-square rectangle 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.
Isosceles triangle, arrow, kite. Which also belongs?
Answer: Isosceles trapezoid (1 axis) 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.
The three figures on the left share a property. Pick the figure on the right with that same property.
Answer: A rectangle divided into 6 equal strips, with strips 1, 3, and 5 shaded 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).
Look at the three figures on the left. Find the figure on the right that belongs to the same group.
Answer: A circle divided into 6 equal parts, 2 shaded 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.
The three figures on the left follow a rule. Which figure on the right follows the same rule?
Answer: A shape with 2 curved sides and 2 straight sides 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.
Refer to the figure below. The three scatter plots in the Set display a certain correlation. Which answer plot displays the same correlation?
Answer: Figure A 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.
2 squares share a side; 2 equilateral triangles share a side; 2 regular hexagons share a side. Which also belongs?
Answer: 2 regular octagons share side 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.
The figures on the left share a common feature. Which figure on the right fits with them?
Answer: A shape with exactly 1 line of symmetry 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.
Look at the three figures on the left. Find the answer choice that belongs with them.
Answer: A circle with 7 tick marks evenly spaced 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.
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.
Answer: A hexagon with a small black circle inside touching one side 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.
The three figures on the left are classified together. Which figure on the right fits this classification?
Answer: A 6-pointed star with 3 alternating points shaded 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.

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