SAT Math — lines, angles and triangles, described in words

Geometry on the digital test almost always comes with a figure on screen, and a text-only bank cannot show one. That turns out to be less of a loss than it sounds, because the figure is often the least informative part: what a learner actually needs is the habit of extracting the relationships from it, and here those relationships are stated in words from the start. Every configuration in this set is described completely — which points lie on which line, which angle sits where — so that a reader with no picture can reconstruct it exactly.

The angle work runs through the configurations that recur endlessly. Two lines crossing make two pairs of equal opposite angles, with the four together filling a full turn. A ray leaving a straight line splits a half turn into two angles that sum to a hundred and eighty. A transversal across two parallel lines makes eight angles of only two different sizes, and the entire difficulty is telling which pairs are equal from which pairs add to a straight line — so both questions on it carry the supplement among their wrong options and both explanations name exactly which pair that supplement belongs to.

Three questions concern the angles of a triangle: the three summing to a half turn, an isosceles triangle where the equal sides force equal opposite angles, and an exterior angle formed by extending one side, which equals the two angles it does not touch. That last one has a built-in check worth keeping — the exterior angle and the interior angle beside it must make a straight line, and the three interior angles must still come to a hundred and eighty.

Two questions give a pair of similar triangles with the vertex correspondence stated explicitly, so that identifying which side matches which is part of the work rather than a guess. One wrong option in each comes from applying the scale factor in the wrong direction, producing a triangle larger than the original when it should be smaller; another from pairing sides across the two triangles in the wrong order.

Two turn on the triangle inequality, and both make the same point about the boundary: three lengths where the shorter two add to exactly the longest do not form a triangle, they lie flat. The rule requires strictly greater, and the wrong options are built at and beyond that boundary.

Every point label and name is invented, and nothing is drawn from any official publication.

• Reconstruct a geometric configuration from a description in words, with no figure
• Tell which angles a transversal makes equal from which it makes supplementary
• Use the angle sums of a triangle and a quadrilateral, and the exterior-angle rule, with a check that the whole configuration adds up
• Find a missing angle in an isosceles triangle from the equal sides alone
• Apply a scale factor between similar triangles in the right direction and to the correctly matched sides
• State the triangle inequality precisely, including why equality is not enough

Written for this catalogue, with no source document. The content is the lines, angles and triangles material named in the College Board's own public description of the Geometry and Trigonometry domain — angle relationships, triangle congruence and similarity; every question, option and explanation here is original, and nothing is reproduced from any official publication or released test. Note that the digital test presents most of this material with a figure on screen, which a text-only bank cannot reproduce: every configuration here is instead described completely in words. Zestly is an independent study tool. It is not affiliated with the College Board, which owns the SAT, and it is not an exam centre.