Parallel-line angle relationships, triangle angle sums, similarity and congruence, and the triangle inequality.
75
Total questions
47
Easy
18
Medium
10
Hard
This skill covers the angle-chasing toolkit: vertical angles, parallel lines cut by a transversal, triangle angle sums, exterior angles, isosceles base angles, and similar triangles with proportional sides. Questions often stack several rules in one figure.
Chase angles systematically: mark every angle you can deduce, one rule at a time, rather than hunting for a single clever step. For similar triangles, set up the proportion by matching corresponding vertices in the similarity statement — the order of the letters tells you exactly which sides pair up.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: C
Choice C is correct. By the triangle inequality, the length of each side of a triangle must be less than the sum of the lengths of the other two sides. The third side must therefore be greater than 9 - 4 = 5 and less than 9 + 4 = 13. Since 5 < 10 < 13, a third side of length 10 inches is possible. Choice A is incorrect; if the third side were 4, then 4 + 4 = 8, which is less than 9, so the two shorter sides could not meet to form a triangle. This may result from assuming the third side can be as short as the shortest given side. Choice B is incorrect; 5 is the difference 9 - 4, and a third side of exactly 5 gives 4 + 5 = 9, which is equal to, not greater than, the longest side, so the figure would be flat rather than a triangle. This may result from treating the triangle inequality as 'greater than or equal to' the difference. Choice D is incorrect; 13 is the sum 9 + 4, and a third side of exactly 13 gives 4 + 9 = 13, which is equal to, not greater than, the proposed third side. This may result from treating the triangle inequality as 'less than or equal to' the sum.
Correct answer: D
Choice D is correct. If angle C = 85°, then angle D = 180° - 55° - 85° = 40°. The angles would be 55°, 85°, and 40° — no two are equal, so the triangle is not isosceles. Choice A is incorrect (55°, 55°, 70° is isosceles). Choice B is incorrect (55°, 62.5°, 62.5° is isosceles). Choice C is incorrect (55°, 70°, 55° is isosceles).
Area & Volume
Areas of 2D figures and volumes of 3D solids, including composite shapes and problems where scaling changes area or volume.
Right Triangles & Trigonometry
The Pythagorean theorem, special right triangles, and SOH-CAH-TOA trigonometric ratios, including the sine-cosine complement relationship.
Circles
Circle equations in the xy-plane, arc length, sector area, central angles, and completing the square to find center and radius.
75 Lines, Angles & Triangles questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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