RRB Group D · Bite-size lessons
Geometry
About 6 min · Mathematics · English
Time worked out from the lesson's 360 words at 150 words a minute, plus a minute for each question.
Geometry questions in Railway Group D test your understanding of shapes, angles, and spatial relationships. This topic covers fundamental theorems about lines, angles, triangles, and circles—no complex proofs, but you must recognize properties instantly and apply them to numerical problems.
Key ideas
- Lines and angles: When two lines intersect, vertically opposite angles are equal. When a transversal cuts parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-interior angles sum to 180°.
- Triangle angle-sum property: The three interior angles of any triangle always sum to 180°. An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
- Triangle congruence: Two triangles are congruent if they satisfy SSS (three sides equal), SAS (two sides and included angle), ASA (two angles and included side), or RHS (right angle, hypotenuse, one side) criteria.
- Pythagoras theorem: In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides: c² = a² + b². Common Pythagorean triplets: (3,4,5), (5,12,13), (8,15,17), (7,24,25).
- Circle angle theorems: The angle subtended by an arc at the center is double the angle subtended at any point on the circle. Angles in the same segment are equal. Angle in a semicircle is 90°.
Quick reference
- Vertically opposite angles are always equal.
- Parallel lines + transversal: corresponding equal, alternates equal, co-interior sum = 180°.
- Triangle angles always sum to 180°; exterior angle = sum of remote interiors.
- Pythagoras: c² = a² + b² (right triangles only); know triplets (3,4,5), (5,12,13).
- Circle: center angle = 2 × circumference angle; angle in semicircle = 90°.
Check yourself: 3 questions
1. Two parallel lines are cut by a transversal. If one of the alternate interior angles is 65 degrees, what is the measure of its alternate interior angle?
2. In a triangle ABC, angle A = 50 degrees and angle B = 60 degrees. What is the measure of angle C?
3. A chord of length 16 cm is at a distance of 6 cm from the center of a circle. What is the radius 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.
Read the full noteFlashcards for this topic
Saves this lesson and its 3 questions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.