SAT Lines, Angles, and Triangles Questions
Angle rules, and similar and congruent triangles.
In short
- Lines, Angles, and Triangles is part of Geometry and Trigonometry, about 15% of the scored Math questions: 5 to 7 on every test.
- Math questions from all four areas are mixed in each module and arranged from easiest to hardest.
- Distance missing sqrt is the trap Rivie's practice tests set most often in Lines, Angles, and Triangles questions.
Common traps
Most common first, from Rivie's ten practice tests.
Distance missing sqrt
Distance between two points is √((Δx)² + (Δy)²); the wrong choice computes (Δx)² + (Δy)² and stops without taking the square root.
The usual mistake: You get an integer sum like 25 and pick that, not noticing the question asked for distance, which would be 5.
Similar triangle: segment vs. whole
When a triangle is split by a line parallel to one side, the resulting two triangles are similar, but proportions are between corresponding WHOLE sides, not whole-to-segment.
The usual mistake: You set up a ratio mixing a small triangle's side with a segment of the larger triangle's side. The fix is to mark the two whole triangles' corresponding sides explicitly.
Triangle angle sum
Interior angles of a triangle sum to 180°. The wrong choice misapplies this: using 360°, treating an exterior angle as interior, or forgetting that an isosceles triangle has two equal angles.
The usual mistake: You add the two given angles and subtract from 360° (a quadrilateral rule), or pick the supplement of an exterior angle without converting back.
Try a question
From Rivie's practice tests. Pick an answer to see why it is right or wrong.
In triangle ABC, point D lies on side AB and point E lies on side AC so that segment DE is parallel to segment BC. AD = 8, DB = 12, and AE = 6. What is the length of segment EC?
Video lessons
Free on YouTube, picked for this topic.