Home › Certifications › High School Geometry › Probability and Geometry
14 multiple-choice questions and 5 flashcards on Probability and Geometry, about 9% of the High School Geometry bank. Every one carries a written rationale.
Probability and Geometry is one of 13 chapters in CoStudy's High School Geometry bank, and it holds 14 of the bank's 150 multiple-choice questions — roughly 9% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
5 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
The locus of points equidistant from two given points A and B is:
Answer: E — Perpendicular bisector of AB
Definition of perpendicular bisector. Used in geometric constructions (e.g., finding circumcenter). Constructive geometry: locus of equidistant points = perpendicular bisector of segment.
The Pythagorean theorem states for a right triangle with legs a, b and hypotenuse c:
Answer: C — a² + b² = c² (sum of squares of legs equals square of hypotenuse)
Pythagorean theorem: in right triangle, leg² + leg² = hypotenuse². Fundamental geometric relationship. Converse: if a²+b²=c², triangle is right-angled. Foundation for distance formula and trigonometry.
Two triangles are CONGRUENT if:
Answer: B — Same shape AND same size (corresponding sides and angles equal) — proven via SSS, SAS, ASA, AAS, HL
Congruent ≡ identical shape AND size. Proof methods: SSS (3 sides equal), SAS (2 sides + included angle), ASA (2 angles + included side), AAS (2 angles + non-included side), HL (right triangles). NOT SSA (ambiguous case).
The midpoint of (2, 4) and (8, 10) is:
Answer: B — (5, 7) — midpoint = ((2+8)/2, (4+10)/2) = (5, 7)
Midpoint formula: M = ((x₁+x₂)/2, (y₁+y₂)/2). Average of x's, average of y's. (5, 7). Used for bisecting segments. Coordinate geometry basics.
In a right triangle with legs 6 and 8, what is the hypotenuse?
Answer: B — 10 (Pythagorean: √(36+64) = √100 = 10; classic 6-8-10 triangle, 2× of 3-4-5)
6-8-10 is 2× of 3-4-5 Pythagorean triple. Verify: 6²+8²=36+64=100=10². Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25, plus multiples. Recognize for quick calculation.
4 cards from the 5 in this chapter.
What's the slope formula?
m = (y₂−y₁)/(x₂−x₁).
What's the distance formula?
d = √[(x₂−x₁)² + (y₂−y₁)²].
What's the midpoint formula?
M = ((x₁+x₂)/2, (y₁+y₂)/2).
Find distance between (1, 2) and (4, 6).
5. √(9 + 16) = √25 = 5.
These are a sample. The full Probability and Geometry chapter runs 19 items with per-chapter progress tracking, on the web and in the iOS app.
Open High School Geometry in CoStudy →