MATD113
Geometry 1
Quick Rules
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Time limit: 50 minutes
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Multiple attempts are not allowed
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All questions must be answered to submit
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Question 1
What is the definition of a point in geometry?
Explanation
A point is defined as a location with no size or dimension, serving as a fundamental concept in geometry.
Question 2
Which shape has three sides?
Explanation
A triangle is defined as a polygon with three edges and three vertices.
Question 3
What do we call a closed figure formed by straight lines?
Explanation
A polygon is defined as a closed figure formed by a finite number of straight line segments.
Question 4
What is the sum of the interior angles of a triangle?
Explanation
The sum of the interior angles of a triangle is always 180 degrees.
Question 5
Which of the following statements describes a rectangle?
Explanation
A rectangle is defined as a quadrilateral with opposite sides that are equal and all angles that are right angles.
Question 6
A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. Determine the type of triangle based on its sides. What can you conclude about the relationship between the sides in this triangle?
Explanation
The correct answer is that it is a right triangle because it satisfies the Pythagorean theorem. The sum of the squares of the two shorter sides (5^2 + 12^2) equals the square of the longest side (13^2). The other options misconstrue the properties of triangles regarding congruent sides and types.
Question 7
A rectangle has a length of 10 cm and a width of 4 cm. If you were to double both dimensions, how would that affect the area of the rectangle? Choose the most accurate statement about the relationship between the dimensions and the area.
Explanation
The correct answer is that the area increases by a factor of four. When both dimensions are doubled, the area is calculated as (2 * length) * (2 * width), which results in an area four times larger than the original. The other options incorrectly apply the relationship between dimensions and area, leading to misunderstandings about how area scales.
Question 8
[Case Scenario] A rectangular garden has a length of 20 meters and a width of 15 meters. The owner wants to add a path of uniform width around the garden. After completing the path, the total area of the garden plus the path was found to be 400 square meters. Question: What is the width of the path added around the garden?
Explanation
To find the width of the path, we start with the garden's area of 300 square meters. By letting x be the width of the path, the total area can be expressed as (20 + 2x)(15 + 2x) = 400. Solving this yields a width of approximately 5 meters, in line with the correct analysis.
Question 9
[Case Scenario] A triangle has two sides measuring 8 cm and 6 cm, with an included angle of 50 degrees. A student is tasked to calculate the area of the triangle using the formula Area = 0.5 * a * b * sin(C), where a and b are sides, and C is the included angle. Question: What is the area of the triangle?
Explanation
The correct area is calculated by accurately applying the formula with the given values. The numerical computation leads to approximately 24.56 cm² as the valid area for the triangle based on the angle and side measurements.
Question 10
[Case Scenario] A circular park has a circumference of 62.83 meters. The city council is planning to fence the park and wants to know the radius to estimate the amount of fencing required. The formula for circumference of a circle is C = 2 * π * r, where r is the radius. Question: What is the radius of the circular park?
Explanation
Finding the radius involves rearranging the circumference formula to solve for r: r = C/(2π). Substituting in the circumference gives us a radius of approximately 10 meters, which is the correct dimension for the circular park based on the given circumference.