Chapter 4: Geometry — Online MCQ Test
MATHS · CLASS 10th · Tamil Nadu State Board
Practice Chapter 4: Geometry with a free chapter-wise online MCQ test.
This chapter covers: Thales theorem Angle Bisector theorem Pythagoras theorem Similar triangles Tangent Circle Construction Concurrent lines Median Altitude Perpendicular bisector Geometric proof.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter 4: Geometry — Important Questions & Answers
In a triangle, a line drawn parallel to one side intersects the other two sides. Which theorem states that these two sides are divided in the same ratio?
- A. Thales theorem
- B. Pythagoras theorem
- C. Angle bisector theorem
- D. Median theorem
Answer: A. Thales theorem
Thales theorem, also called the Basic Proportionality Theorem, states that a line parallel to one side of a triangle divides the other two sides proportionally.
Thales theorem, also called the Basic Proportionality Theorem, states that a line parallel to one side of a triangle divides the other two sides proportionally.
In triangle ABC, AD is the internal angle bisector of angle A meeting BC at D. According to the angle bisector theorem, which relation is true?
- A. AB/AC = BD/DC
- B. AB/BC = AC/DC
- C. BD/AB = DC/BC
- D. AB + AC = BD + DC
Answer: A. AB/AC = BD/DC
The angle bisector theorem says that an internal angle bisector divides the opposite side in the ratio of the adjacent sides.
The angle bisector theorem says that an internal angle bisector divides the opposite side in the ratio of the adjacent sides.
In triangle ABC, D lies on AB and E lies on AC. If DE is parallel to BC, AD = 4 cm, DB = 6 cm and AE = 6 cm, then EC is:
- A. 4 cm
- B. 6 cm
- C. 9 cm
- D. 10 cm
Answer: C. 9 cm
By Thales theorem, AD/DB = AE/EC. So 4/6 = 6/EC, giving EC = 9 cm.
By Thales theorem, AD/DB = AE/EC. So 4/6 = 6/EC, giving EC = 9 cm.
In triangle ABC, D lies on AB and E lies on AC. If DE is parallel to BC, AD = 3 cm, DB = 2 cm and AE = 4.5 cm, then AC is:
- A. 6 cm
- B. 7.5 cm
- C. 8 cm
- D. 9 cm
Answer: B. 7.5 cm
Since DE is parallel to BC, AD/AB = AE/AC. Here AB = 5 cm, so 3/5 = 4.5/AC, giving AC = 7.5 cm.
Since DE is parallel to BC, AD/AB = AE/AC. Here AB = 5 cm, so 3/5 = 4.5/AC, giving AC = 7.5 cm.
In triangle ABC, D lies on AB and E lies on AC such that DE is parallel to BC. If AD : DB = 2 : 3 and the area of quadrilateral DBCE is 84 cm², then the area of triangle ADE is:
- A. 12 cm²
- B. 16 cm²
- C. 20 cm²
- D. 24 cm²
Answer: B. 16 cm²
Since AD : AB = 2 : 5, area of triangle ADE : area of triangle ABC = 4 : 25. Thus the quadrilateral is 21 parts = 84, so 1 part = 4 and area of triangle ADE = 16 cm².
Since AD : AB = 2 : 5, area of triangle ADE : area of triangle ABC = 4 : 25. Thus the quadrilateral is 21 parts = 84, so 1 part = 4 and area of triangle ADE = 16 cm².