This skill evaluation ⚡ worksheet focuses on Geometry - Triangles - a key topic in Data Sufficiency. You'll solve 20 expert-level problems (Worksheet 9 of 10). The primary focus is on conceptual clarity. Master geometry - triangles ssc cgl, geometry - triangles reasoning tricks, and fast geometry - triangles solving through systematic practice.
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Your progress through Geometry - Triangles
Worksheet 9 of 10 (88% complete)
Question 1
Question: Is triangle ABC equilateral?
Statement (1): AB = BC
Statement (2): Angle B = 60°
From (1): Isosceles triangle with AB = BC. From (2): Angle B = 60°. In isosceles triangle with vertex angle 60°, base angles are (180-60)/2 = 60° each → equilateral.
Question 2
Question: Is triangle ABC equilateral?
Statement (1): AB = BC
Statement (2): Angle B = 60°
From (1): Isosceles triangle with AB = BC. From (2): Angle B = 60°. In isosceles triangle with vertex angle 60°, base angles are (180-60)/2 = 60° each → equilateral.
Question 3
Question: Is triangle ABC a right triangle?
Statement (1): Sides are 3, 4, and 5 units.
Statement (2): Angles are in the ratio 1:2:3.
Statement (1): 3² + 4² = 9 + 16 = 25 = 5², satisfies Pythagoras → right triangle. Statement (2): Angles sum to 180°, ratio 1:2:3 gives angles 30°, 60°, 90° → right triangle.
Question 4
Question: What is the area of triangle ABC?
Statement (1): Base BC = 8 cm
Statement (2): Height from A to BC = 5 cm
Area = (1/2) × base × height = (1/2) × 8 × 5 = 20 cm².
Question 5
Question: What is the perimeter of triangle ABC?
Statement (1): AB = 5 cm, BC = 7 cm
Statement (2): Triangle is isosceles with AC as base
Even together, we don't know if AB = AC or BC = AC. Multiple possibilities exist.
Question 6
Question: Is triangle ABC a right triangle?
Statement (1): Sides are 3, 4, and 5 units.
Statement (2): Angles are in the ratio 1:2:3.
Statement (1): 3² + 4² = 9 + 16 = 25 = 5², satisfies Pythagoras → right triangle. Statement (2): Angles sum to 180°, ratio 1:2:3 gives angles 30°, 60°, 90° → right triangle.
Question 7
Question: Is triangle ABC equilateral?
Statement (1): AB = BC
Statement (2): Angle B = 60°
From (1): Isosceles triangle with AB = BC. From (2): Angle B = 60°. In isosceles triangle with vertex angle 60°, base angles are (180-60)/2 = 60° each → equilateral.
Question 8
Question: Is triangle ABC equilateral?
Statement (1): AB = BC
Statement (2): Angle B = 60°
From (1): Isosceles triangle with AB = BC. From (2): Angle B = 60°. In isosceles triangle with vertex angle 60°, base angles are (180-60)/2 = 60° each → equilateral.
Question 9
Question: Is triangle ABC a right triangle?
Statement (1): Sides are 3, 4, and 5 units.
Statement (2): Angles are in the ratio 1:2:3.
Statement (1): 3² + 4² = 9 + 16 = 25 = 5², satisfies Pythagoras → right triangle. Statement (2): Angles sum to 180°, ratio 1:2:3 gives angles 30°, 60°, 90° → right triangle.
Question 10
Question: What is the area of triangle ABC?
Statement (1): Base BC = 8 cm
Statement (2): Height from A to BC = 5 cm
Area = (1/2) × base × height = (1/2) × 8 × 5 = 20 cm².
Question 11
Question: Is triangle ABC a right triangle?
Statement (1): Sides are 3, 4, and 5 units.
Statement (2): Angles are in the ratio 1:2:3.
Statement (1): 3² + 4² = 9 + 16 = 25 = 5², satisfies Pythagoras → right triangle. Statement (2): Angles sum to 180°, ratio 1:2:3 gives angles 30°, 60°, 90° → right triangle.
Question 12
Question: What is the perimeter of triangle ABC?
Statement (1): AB = 5 cm, BC = 7 cm
Statement (2): Triangle is isosceles with AC as base
Even together, we don't know if AB = AC or BC = AC. Multiple possibilities exist.
Question 13
Question: What is the perimeter of triangle ABC?
Statement (1): AB = 5 cm, BC = 7 cm
Statement (2): Triangle is isosceles with AC as base
Even together, we don't know if AB = AC or BC = AC. Multiple possibilities exist.
Question 14
Question: What is the perimeter of triangle ABC?
Statement (1): AB = 5 cm, BC = 7 cm
Statement (2): Triangle is isosceles with AC as base
Even together, we don't know if AB = AC or BC = AC. Multiple possibilities exist.
Question 15
Question: What is the area of triangle ABC?
Statement (1): Base BC = 8 cm
Statement (2): Height from A to BC = 5 cm
Area = (1/2) × base × height = (1/2) × 8 × 5 = 20 cm².
Question 16
Question: Is triangle ABC equilateral?
Statement (1): AB = BC
Statement (2): Angle B = 60°
From (1): Isosceles triangle with AB = BC. From (2): Angle B = 60°. In isosceles triangle with vertex angle 60°, base angles are (180-60)/2 = 60° each → equilateral.
Question 17
Question: What is the perimeter of triangle ABC?
Statement (1): AB = 5 cm, BC = 7 cm
Statement (2): Triangle is isosceles with AC as base
Even together, we don't know if AB = AC or BC = AC. Multiple possibilities exist.
Question 18
Question: What is the area of triangle ABC?
Statement (1): Base BC = 8 cm
Statement (2): Height from A to BC = 5 cm
Area = (1/2) × base × height = (1/2) × 8 × 5 = 20 cm².
Question 19
Question: Is triangle ABC a right triangle?
Statement (1): Sides are 3, 4, and 5 units.
Statement (2): Angles are in the ratio 1:2:3.
Statement (1): 3² + 4² = 9 + 16 = 25 = 5², satisfies Pythagoras → right triangle. Statement (2): Angles sum to 180°, ratio 1:2:3 gives angles 30°, 60°, 90° → right triangle.
Question 20
Question: Is triangle ABC a right triangle?
Statement (1): Sides are 3, 4, and 5 units.
Statement (2): Angles are in the ratio 1:2:3.
Statement (1): 3² + 4² = 9 + 16 = 25 = 5², satisfies Pythagoras → right triangle. Statement (2): Angles sum to 180°, ratio 1:2:3 gives angles 30°, 60°, 90° → right triangle.
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