Geometry
About 6 min · Mathematics · English
Time worked out from the lesson's 417 words at 150 words a minute, plus a minute for each question.
Geometry is part of the Mathematics section in AP TET Paper I and Paper II. Questions test your understanding of spatial relationships, properties of shapes, and ability to apply theorems to solve problems.
Key ideas
- Point, Line, Ray, Line Segment: A point has no dimension. A line extends infinitely in both directions. A ray has one endpoint and extends infinitely in one direction. A line segment has two endpoints with definite length.
- Types of Angles: Acute (less than 90°), Right (exactly 90°), Obtuse (between 90° and 180°), Straight (exactly 180°), Reflex (between 180° and 360°), Complete (exactly 360°).
- Angle Relationships: Complementary angles sum to 90°. Supplementary angles sum to 180°. Vertically opposite angles are equal. Adjacent angles share a common arm.
- Parallel Lines and Transversal: When a transversal cuts parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-interior (same-side interior) angles are supplementary.
- Triangle Properties: Sum of interior angles equals 180°. Exterior angle equals sum of two non-adjacent interior angles. Sum of any two sides is greater than the third side.
Watch out for
- Confusing alternate and corresponding angles: Alternate angles are on opposite sides of the transversal (Z-pattern). Corresponding angles are on the same side (F-pattern). Draw the pattern to identify correctly.
- Forgetting exterior angle theorem direction: The exterior angle equals the sum of the two remote (non-adjacent) interior angles, not the adjacent one. Students often add the wrong pair.
- Using wrong formula for polygon angles: For interior angle sum, use (n − 2) × 180°. For exterior angle sum, it is always 360° regardless of the number of sides. Mixing these leads to wrong answers.
Quick reference
- Angle sum in triangle = 180°; in quadrilateral = 360°
- Parallel lines + transversal: Corresponding angles equal, alternate angles equal, co-interior angles = 180°
- Exterior angle of triangle = sum of two non-adjacent interior angles
- Regular polygon interior angle = (n − 2) × 180° ÷ n
- Pythagoras: a² + b² = c² (only for right triangles)
Check yourself: 3 questions
1. In a triangle ABC, if angle A = 50 degrees and angle B = 60 degrees, what is the measure of angle C?
2. Two parallel lines are cut by a transversal. If one of the alternate interior angles measures 65 degrees, what is the measure of the other alternate interior angle?
3. The sum of the interior angles of a polygon is 1080 degrees. How many sides does the polygon have?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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