Geometry for 7th Graders: Master Shapes and Measurements

Question 1

What are the four types of angles based on their measure?

Accepted Answer

Acute, right, obtuse, and straight

Answer

Acute, obtuse, reflex, and straight

Answer

Small, medium, large, and extra large

Answer

Positive, negative, zero, and undefined

Question 2

Question: Define congruent figures and explain their key properties.

Accepted Answer

Congruent figures have the same size and shape, regardless of their orientation.

Answer

Option 1: Congruent figures have different sizes and shapes but the same color.

Question 3

Which polygon has 6 sides and 6 angles?

Accepted Answer

Hexagon

Answer

Triangle

Answer

Square

Answer

Octagon

Question 4

A circle has a radius of 5 centimeters. What is its diameter?

Accepted Answer

10 centimeters

Answer

2.5 centimeters

Answer

20 centimeters

Answer

50 centimeters

Question 5

What makes a parallelogram unique? Describe the properties that distinguish it from other quadrilaterals.

Accepted Answer

Two pairs of parallel sides and two pairs of congruent angles

Answer

Only one pair of parallel sides

Answer

All four angles are right angles

Question 6

When two straight lines meet at a common endpoint, what shape is created?

Accepted Answer

Angle

Answer

Point

Answer

Triangle

Answer

Line segment

Question 7

Which of the following is NOT a characteristic of a triangle?

Accepted Answer

Has two obtuse angles

Answer

Has three sides

Answer

Has three vertices

Answer

Has three angles that add up to 180 degrees

Question 8

What is the formula for calculating the area of a triangle?

Accepted Answer

Base x Height / 2

Answer

Length x Width

Answer

Pi x Radius^2

Answer

4/3 x Pi x Radius^3

Question 9

Which type of angle measures less than 90 degrees?

Accepted Answer

Acute angle

Answer

Right angle

Answer

Obtuse angle

Answer

Straight angle

Question 10

Which of these is an example of a three-dimensional shape?

Accepted Answer

Cube

Answer

Square

Answer

Circle

Answer

Line segment

Question 11

Which of these is NOT a basic geometric shape?

Accepted Answer

Star

Answer

Triangle

Answer

Square

Answer

Circle

Question 12

What is the term used for a straight line segment that connects two points?

Accepted Answer

Segment

Answer

Ray

Answer

Line

Answer

Vector

Question 13

Which type of angle measures less than 90 degrees?

Accepted Answer

Acute angle

Answer

Right angle

Answer

Obtuse angle

Answer

Straight angle

Question 14

Calculate the area of a triangle with a base of 5 cm and a height of 3 cm?

Accepted Answer

7.5 cm²

Answer

5 cm²

Answer

15 cm²

Answer

10 cm²

Question 15

What is the sum of the interior angles of a triangle?

Accepted Answer

180 degrees

Answer

120 degrees

Answer

270 degrees

Answer

360 degrees

Question 16

What is the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a + b = c

Answer

a x b = c

Question 17

Which of these is NOT a basic geometric concept introduced in this unit?

Accepted Answer

Rectangle

Answer

Point

Answer

Line

Answer

Angle

Question 18

Which of these shapes has four congruent sides and four right angles?

Accepted Answer

Square

Answer

Triangle

Answer

Rectangle

Answer

Circle

Question 19

What is the formula used to calculate the area of a triangle?

Accepted Answer

A = ½ × base × height

Answer

A = πr²

Answer

A = s × h

Answer

A = 4/3πr³

Question 20

Which formula is used to calculate the volume of a rectangular prism?

Accepted Answer

V = l × w × h

Answer

V = πr²h

Answer

V = s × h

Answer

V = 4/3πr³

Question 21

Which property describes a circle?

Accepted Answer

All points on the circle are equally distant from the center

Answer

The circumference is equal to π × diameter

Answer

It has endpoints

Answer

It has sides

Question 22

Which of these is a two-dimensional shape?

Accepted Answer

Triangle

Answer

Sphere

Answer

Cube

Answer

Cylinder

Question 23

Which shape is an example of a fractal?

Accepted Answer

Koch snowflake

Answer

Square

Answer

Circle

Answer

Triangle

Question 24

In geometry, which tool is essential for drawing precise circles and arcs?

Accepted Answer

Compass

Answer

Protractor

Answer

Calculator

Question 25

What makes parallelograms unique among quadrilaterals? Define parallelograms and explain how their distinct features set them apart.

Accepted Answer

Parallelograms have two pairs of parallel sides.

Answer

Parallelograms have four right angles.

Answer

Parallelograms have two pairs of equal sides.

Answer

Parallelograms have two pairs of equal angles.

Question 26

A circular garden has a circumference of 31.4 cm. What's the garden's area?

Accepted Answer

78.5 cm²

Answer

157 cm²

Answer

39.25 cm²

Answer

12.56 cm²

Question 27

When two straight lines intersect at a shared endpoint, they create an angle. Categorize angles based on their measurements and provide examples of each category.

Accepted Answer

Acute, Right, Obtuse

Answer

Small, Medium, Large

Answer

Convex, Concave, Reflex

Answer

Positive, Negative, Zero

Question 28

In a triangle, the number of sides is three. What is the sum of its interior angles?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 29

Which shape has only rotational symmetry, but no reflectional symmetry?

Accepted Answer

Circle

Answer

Square

Answer

Rectangle

Answer

Triangle

Question 30

Identify the key characteristics that define a parallelogram:

Accepted Answer

Opposite sides are parallel and equal in length

Accepted Answer

Opposite angles add up to 180 degrees

Accepted Answer

It has two pairs of equal angles

Answer

All four sides have the same length

Question 31

In a right triangle, what theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides?

Accepted Answer

Pythagorean Theorem

Answer

Triangle Theorem

Answer

Hypotenuse Theorem

Question 32

Which condition is NOT required for two triangles to be similar?

Accepted Answer

The triangles have the same number of sides.

Answer

Corresponding angles are congruent.

Answer

Corresponding sides are proportional.

Question 33

What is geometric modeling, and how is it used in engineering and design?

Accepted Answer

Geometric modeling is a technique for creating 3D models of objects using computer software. These models can be used in computer-aided design (CAD) software to create blueprints for buildings, products, and other objects.

Answer

Geometric modeling is only used in computer-aided design (CAD) software.

Answer

Geometric models are not used in 3D printing.

Answer

Geometric modeling has no practical applications.

Question 34

Which shape has 4 equal sides and 4 right angles?

Accepted Answer

Rectangle

Answer

Trapezoid

Answer

Rhombus

Answer

Parallelogram

Question 35

What is coordinate geometry and how is it used in graphing equations, finding distances, and solving geometric problems?

Accepted Answer

Coordinate geometry is a way to represent geometric figures using numbers and equations. It's used to graph equations, find distances, and solve geometric problems.

Answer

Coordinate geometry is only used to find the area of triangles.

Answer

Coordinate geometry is only used to graph equations.

Answer

Coordinate geometry is a branch of algebra that uses numbers to represent geometric figures.

Question 36

In quadrilateral PQRS, what is the sum of its interior angles?

Accepted Answer

360 degrees

Answer

180 degrees

Answer

270 degrees

Answer

450 degrees

Question 37

Which polygon has exactly six sides?

Accepted Answer

Hexagon

Answer

Triangle

Answer

Quadrilateral

Answer

Octagon

Question 38

What is the formula to calculate the area of a rectangle?

Accepted Answer

Length x Width

Answer

Length + Width

Answer

Length / Width

Answer

2 x Length x 2 x Width

Question 39

What is the measurement of an angle that is half of a right angle?

Accepted Answer

45 degrees

Answer

22.5 degrees

Answer

67.5 degrees

Answer

90 degrees

Question 40

Which characteristic describes a circle?

Accepted Answer

Has a circumference

Answer

Has parallel sides

Answer

Has right angles

Answer

Has 4 equal sides

Question 41

What is the formula to find the perimeter of a square?

Accepted Answer

4 x side length

Answer

2 x side length

Answer

side length + side length + side length + side length

Answer

side length x side length

Question 42

Which shape is three-dimensional?

Accepted Answer

Sphere

Answer

Triangle

Answer

Rectangle

Answer

Pentagon

Question 43

What is the sum of the interior angles of a triangle?

Accepted Answer

180 degrees

Answer

270 degrees

Answer

360 degrees

Answer

540 degrees

Question 44

Which term describes a line segment that has two endpoints but extends infinitely in one direction?

Accepted Answer

Ray

Answer

Chord

Answer

Tangent

Answer

Vector

Question 45

What is the name of the point where two or more lines meet?

Accepted Answer

Vertex

Answer

Midpoint

Answer

Circumcenter

Answer

Incenter

Question 46

A circle has an area of 36π square centimeters. Calculate its radius and circumference.

Accepted Answer

Radius: 6 cm, Circumference: 12π cm

Answer

Radius: 3 cm, Circumference: 6π cm

Answer

Radius: 9 cm, Circumference: 18π cm

Answer

Radius: 12 cm, Circumference: 24π cm

Question 47

In a circle, a central angle of 60 degrees intercepts an arc of length 12 cm. Find the radius of the circle.

Accepted Answer

6 cm

Answer

12 cm

Answer

24 cm

Question 48

Which of the following is NOT a basic geometric shape?

Accepted Answer

Heart

Answer

Triangle

Answer

Square

Answer

Rectangle

Question 49

What is the point where two lines meet called?

Accepted Answer

Point

Answer

Line

Answer

Angle

Answer

Curve

Question 50

Which type of angle is smaller than a right angle?

Accepted Answer

Acute angle

Answer

Right angle

Answer

Obtuse angle

Answer

Straight angle

Question 51

What is the formula to find the area of a triangle?

Accepted Answer

A = (1/2) * base * height

Answer

A = l * w

Answer

A = πr²

Answer

A = 4/3 * πr³

Question 52

Which of the following is a key property of a circle?

Accepted Answer

All points on the circle are the same distance from the center.

Answer

A circle has two parallel sides.

Answer

The diameter of a circle is always smaller than its radius.

Answer

A circle has six right angles.

Question 53

Which of the following shapes is similar to a cone?

Accepted Answer

Pyramid

Answer

Sphere

Answer

Cube

Answer

Cylinder

Question 54

What is the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a + b = c

Answer

a/b = c

Answer

a - b = c

Question 55

Which geometric transformation does not change the size or shape of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 56

What is the theorem that states that the sum of the interior angles of a triangle is 180 degrees called?

Accepted Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Circle Theorem

Answer

Area Theorem

Question 57

What is a vertex?

Accepted Answer

The point where two or more lines intersect

Answer

A shape with four sides

Answer

A curved line

Answer

A shape with three sides

Question 58

How many degrees are in a straight angle?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Question 59

What is the formula for the area of a triangle?

Accepted Answer

1/2 * base * height

Answer

4/3 * π * radius^3

Answer

Length * width

Question 60

What is a defining characteristic of a circle?

Accepted Answer

All points are the same distance from the center

Answer

Has two diagonals

Answer

Has four sides

Question 61

Which of the following is a type of quadrilateral?

Accepted Answer

Rectangle

Answer

Heptagon

Answer

Sphere

Question 62

What is the volume of a rectangular prism with a length of 5 cm, a width of 3 cm, and a height of 2 cm?

Accepted Answer

30 cubic cm

Answer

60 cubic cm

Answer

120 cubic cm

Question 63

What is an example of a transformational geometry?

Accepted Answer

Translation

Answer

Multiplication

Answer

Addition

Question 64

which of these is not considered a basic 2D geometric shape?

Accepted Answer

Sphere

Answer

Circle

Answer

Triangle

Answer

Square