Practice Test
Plane Geometry 1
Quick Rules
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Time limit: 10 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 basic definition of a plane in geometry?
Explanation
A plane is defined as a flat surface that extends infinitely in all directions, with no thickness.
Question 2
In plane geometry, 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, which is a fundamental property of triangles in plane geometry.
Question 3
What type of triangle has three sides of equal length?
Explanation
An equilateral triangle is defined as having three sides of equal length, while an isosceles triangle has two equal sides.
Question 4
Which of the following shapes has four sides?
Explanation
A quadrilateral is defined as a polygon with four sides, while a hexagon has six sides, a triangle has three, and a pentagon has five.
Question 5
What is the formula for calculating the area of a rectangle?
Explanation
The area of a rectangle is calculated using the formula Length × Width, which multiplies the length and width of the rectangle.
Question 6
A triangle has angles measuring 40 degrees, 70 degrees, and x degrees. If the triangle is similar to another triangle with angles measuring y degrees, 40 degrees, and z degrees, what is the value of x, and how does it relate to the angles of the second triangle?
Explanation
The correct answer is that x is 70 degrees; in similar triangles, corresponding angles are equal. Given that the first triangle has two angles of 40 degrees and 70 degrees, it follows that the third angle must also be 70 degrees to maintain similarity with the second triangle.
Question 7
In a square garden, each side measures 10 meters. A path of 1-meter width is constructed inside the garden along its perimeter. What would be the area of the remaining garden after the path is built, and how does this calculation connect to the concepts of area and perimeter?
Explanation
The correct calculation shows that with the path, each dimension of the square garden is effectively reduced by 2 meters (1 meter for each side), leading to an area of 8 meters by 8 meters, giving an area of 64 square meters. This highlights the relationship between perimeter reductions and area calculations.
Question 8
[Case Scenario] A right-angled triangle has one leg measuring 3 cm and the other leg measuring 4 cm. The triangle is placed on a coordinate plane such that one vertex is at the origin (0,0), one leg lies along the x-axis, and the other leg is perpendicular to it along the y-axis. The hypotenuse is opposite the right angle. What is the length of the hypotenuse of this triangle? Question: What is the length of the hypotenuse of the triangle?
Explanation
The hypotenuse of a right-angled triangle can be calculated using the Pythagorean theorem, which states that the sum of the squares of the legs equals the square of the hypotenuse. Hence, the correct hypotenuse length is 5 cm.
Question 9
[Case Scenario] A rectangle has a length of 10 cm and a width of 5 cm. The rectangle is divided into smaller squares of equal size. If the smaller squares have a side length of 2 cm, how many complete squares can fit inside the rectangle? Question: How many complete squares can fit inside the rectangle?
Explanation
Calculating how many squares fit in the rectangle involves dividing the total area of the rectangle by the area of one square, yielding 12 complete squares as the largest integer value fitting within the defined space.
Question 10
[Case Scenario] A circle has a radius of 7 cm. A chord of this circle is drawn such that it is 6 cm away from the center of the circle. Calculate the length of the chord. Question: What is the length of the chord drawn in the circle?
Explanation
Using the properties of a circle, the length of the chord can be determined using the relationship involving the radius and the perpendicular distance from the center to the chord, resulting in chords of length 10 cm.