Expressing Geometric Properties with Equations Practice Questions
Common Core (US) · Common Core Geometry · 141 free MCQs with instant results and detailed explanations.
141
Total
44
Easy
73
Medium
24
Hard
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Sample Questions from Expressing Geometric Properties with Equations
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Q1
Easy
If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, which of the following statements is true?
A.
The triangle is a right triangle.
B.
The triangle is an equilateral triangle.
C.
The triangle is an isosceles triangle.
D.
The triangle is a scalene triangle.
Show Answer & Explanation
Correct Answer: A
A triangle is a right triangle if it satisfies the Pythagorean theorem. For sides 3 cm, 4 cm, and 5 cm, 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25, confirming it is a right triangle.
Q2
Easy
What is the perimeter of a rectangle with a length of 8 cm and a width of 5 cm?
A.
26 cm
B.
40 cm
C.
30 cm
D.
16 cm
Show Answer & Explanation
Correct Answer: A
The perimeter of a rectangle is calculated using the formula P = 2(l + w). Here, length (l) is 8 cm and width (w) is 5 cm. Thus, P = 2(8 + 5) = 2(13) = 26 cm.
Q3
Easy
What is the perimeter of a rectangle with a length of 8 units and a width of 3 units?
A.
22 units
B.
24 units
C.
16 units
D.
30 units
Show Answer & Explanation
Correct Answer: A
The perimeter of a rectangle is calculated using the formula P = 2(length + width). Here, P = 2(8 + 3) = 2(11) = 22 units.
Q4
Medium
Which equation represents the area of a rectangle with length l and width w?
A.
A = l + w
B.
A = 2(l + w)
C.
A = lw
D.
A = l - w
Show Answer & Explanation
Correct Answer: C
The area of a rectangle is calculated as the product of its length and width, thus A = lw is the correct formula.
Q5
Medium
If a triangle has sides of lengths 7 cm, 24 cm, and x cm, what is the range of possible values for x based on the triangle inequality theorem?
A.
5 < x < 31
B.
17 < x < 31
C.
17 < x < 24
D.
24 < x < 31
Show Answer & Explanation
Correct Answer: B
According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side, leading to the inequalities: 7 + 24 > x and x < 7 + 24, which simplifies to 17 < x < 31.
Q6
Medium
Which of the following lines is perpendicular to the line represented by the equation y = -3x + 4?
A.
y = (1/3)x + 2
B.
y = 3x - 1
C.
y = -1/3x + 1
D.
y = 3x + 5
Show Answer & Explanation
Correct Answer: D
The slope of the given line is -3. A line perpendicular to it must have a slope that is the negative reciprocal, which is 1/3. The line with a slope of 3 (option D) is perpendicular since it has a slope that correctly fulfills this criterion.
Q7
Medium
A right triangle has one leg measuring 6 cm and another leg measuring 8 cm. What is the length of the hypotenuse?
A.
10 cm
B.
12 cm
C.
14 cm
D.
15 cm
Show Answer & Explanation
Correct Answer: A
Using the Pythagorean theorem (a² + b² = c²), where a = 6 cm and b = 8 cm, we get 6² + 8² = 36 + 64 = 100, thus c = √100 = 10 cm.
Q8
Hard
A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What type of triangle is it based on the side lengths?
A.
Acute triangle
B.
Right triangle
C.
Obtuse triangle
D.
Equilateral triangle
Show Answer & Explanation
Correct Answer: B
This triangle is a right triangle because it satisfies the Pythagorean theorem: 7^2 + 24^2 = 25^2, which equals 49 + 576 = 625. Since the sum of the squares of the two shorter sides equals the square of the longest side, it confirms that the triangle is right-angled.
Q9
Hard
In a coordinate plane, the vertices of a quadrilateral are A(2, 3), B(6, 3), C(6, 7), and D(2, 7). What type of quadrilateral is ABCD?
A.
Trapezoid
B.
Parallelogram
C.
Rectangle
D.
Rhombus
Show Answer & Explanation
Correct Answer: C
ABCD is a rectangle because opposite sides are equal in length (AB = CD = 4 units and AD = BC = 4 units) and all angles are right angles (the slopes of adjacent sides are perpendicular). Therefore, it meets the definition of a rectangle.
Q10
Hard
A triangle has vertices at points A(2, 3), B(4, 7), and C(6, 3). What is the equation of the line that bisects the angle at vertex A?
A.
y - 3 = 2(x - 2)
B.
y - 3 = -2(x - 2)
C.
y - 3 = (1/2)(x - 2)
D.
y - 3 = (3/2)(x - 2)
Show Answer & Explanation
Correct Answer: A
To find the angle bisector, we first determine the slopes of AB and AC. The slope of AB is (7-3)/(4-2) = 2 and the slope of AC is (3-3)/(6-2) = 0. The angle bisector's slope is the average of these slopes when expressed in the correct format, leading to the equation y - 3 = 2(x - 2).
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Expressing Geometric Properties with Equations — Common Core (US) Common Core Geometry Practice Questions Online
This page contains 141 practice MCQs for the chapter Expressing Geometric Properties with Equations in Common Core (US) Common Core Geometry. The questions are organized by difficulty — 44 easy, 73 medium, 24 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.