Chapter Exam

Chapter 4: Geometry — Online MCQ Test

Q: 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?

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.

Q: 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?

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.

Q: Fill in the blank: In a right triangle with legs a, b and hypotenuse c, Pythagoras theorem is ______.

Answer: B. a² + b² = c² — Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Q: A tangent is drawn to a circle at point P. If O is the centre of the circle, then angle between OP and the tangent at P is:

Answer: C. 90° — The radius drawn to the point of contact is perpendicular to the tangent. Hence the angle is 90°.

Q: 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:

Answer: C. 9 cm — By Thales theorem, AD/DB = AE/EC. So 4/6 = 6/EC, giving EC = 9 cm.

Q: In triangle ABC, AD is the angle bisector of angle A meeting BC at D. If AB = 5 cm, AC = 7 cm and BD = 10 cm, then DC is:

Answer: B. 14 cm — By the angle bisector theorem, AB/AC = BD/DC. Thus 5/7 = 10/DC, so DC = 14 cm.

Q: 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:

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.

Q: Two similar triangles have perimeters 18 cm and 30 cm. If the area of the smaller triangle is 72 cm², then the area of the larger triangle is:

Answer: D. 200 cm² — The ratio of corresponding sides is 18 : 30 = 3 : 5. Hence the area ratio is 9 : 25, so the larger area is 72 × 25/9 = 200 cm².

Q: 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:

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.

Q: In right triangle ABC, angle A = 90°. The angle bisector of angle A meets hypotenuse BC at D. If BD : DC = 3 : 4 and BC = 25 cm, then the area of triangle ABC is:

Answer: C. 150 cm² — By the angle bisector theorem, AB : AC = 3 : 4. Since the hypotenuse is 25 cm, the sides are 15 cm and 20 cm, so area = 1/2 × 15 × 20 = 150 cm².

MATHS · CLASS 10th · Tamil Nadu State Board

Practice Chapter 4: Geometry with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 10th MATHS. 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.

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Chapter 4: Geometry — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 10th MATHS — Chapter 4: Geometry, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

Fill in the blank: In a right triangle with legs a, b and hypotenuse c, Pythagoras theorem is ______.

A. a + b = c
B. a² + b² = c² ✓
C. a² - b² = c²
D. 2ab = c²

Answer: B. a² + b² = c²
Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

A tangent is drawn to a circle at point P. If O is the centre of the circle, then angle between OP and the tangent at P is:

A. 45°
B. 60°
C. 90° ✓
D. 180°

Answer: C. 90°
The radius drawn to the point of contact is perpendicular to the tangent. Hence the angle is 90°.

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.

In triangle ABC, AD is the angle bisector of angle A meeting BC at D. If AB = 5 cm, AC = 7 cm and BD = 10 cm, then DC is:

A. 12 cm
B. 14 cm ✓
C. 15 cm
D. 17 cm

Answer: B. 14 cm
By the angle bisector theorem, AB/AC = BD/DC. Thus 5/7 = 10/DC, so DC = 14 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.

Two similar triangles have perimeters 18 cm and 30 cm. If the area of the smaller triangle is 72 cm², then the area of the larger triangle is:

A. 120 cm²
B. 150 cm²
C. 180 cm²
D. 200 cm² ✓

Answer: D. 200 cm²
The ratio of corresponding sides is 18 : 30 = 3 : 5. Hence the area ratio is 9 : 25, so the larger area is 72 × 25/9 = 200 cm².

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.

In right triangle ABC, angle A = 90°. The angle bisector of angle A meets hypotenuse BC at D. If BD : DC = 3 : 4 and BC = 25 cm, then the area of triangle ABC is:

A. 120 cm²
B. 135 cm²
C. 150 cm² ✓
D. 180 cm²

Answer: C. 150 cm²
By the angle bisector theorem, AB : AC = 3 : 4. Since the hypotenuse is 25 cm, the sides are 15 cm and 20 cm, so area = 1/2 × 15 × 20 = 150 cm².

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