Geometry
About 6 min · Numerical and Mathematical Ability · English
Time worked out from the lesson's 311 words at 150 words a minute, plus a minute for each question.
Unlike higher-level exams, MTS geometry focuses on fundamental theorems and direct application rather than complex proofs. Students must master angle relationships, triangle properties, and circle theorems to solve problems quickly.
Key ideas
- Complementary angles sum to 90°; supplementary angles sum to 180°. Vertically opposite angles formed by intersecting lines are always equal.
- Parallel lines cut by a transversal create corresponding angles (equal), alternate interior angles (equal), and co-interior angles (supplementary at 180°).
- Triangle angle sum is always 180°. An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
- Congruent triangles have identical corresponding sides and angles. Common tests: SSS (3 sides), SAS (2 sides + included angle), ASA (2 angles + included side), RHS (right angle + hypotenuse + side).
- Similar triangles have equal corresponding angles and proportional sides. If two triangles are similar, the ratio of any two corresponding sides is constant.
Quick reference
- Complementary = 90°; Supplementary = 180°; Vertically opposite angles are equal.
- Triangle angles sum = 180°; Exterior angle = sum of two remote interior angles.
- Pythagoras: c² = a² + b² (right triangles only). Know triplets: 3-4-5, 5-12-13, 8-15-17.
- Parallel lines + transversal: corresponding angles equal, alternate interior equal, co-interior sum to 180°.
- Angle in semicircle = 90°; Angle at center = 2 × angle at circumference (same arc).
Check yourself: 3 questions
1. In a triangle ABC, angle A = 50° and angle B = 60°. What is the measure of angle C?
2. Two angles of a triangle are in the ratio 2:3 and the third angle is 80°. What is the measure of the smallest angle of the triangle?
3. In a circle with center O, a chord AB subtends an angle of 80° at the center. What is the angle subtended by the same chord at a point C on the major arc of the circle?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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