Triangles: Master the Basics of Triangles in Geometry

Question 1

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse is equal to:

Accepted Answer

The sum of the squares of the legs

Answer

The difference of the squares of the legs

Answer

The product of the squares of the legs

Answer

The sum of the legs

Question 2

In an isosceles triangle, the angles opposite the congruent sides are called:

Accepted Answer

Equal

Answer

Unequal

Answer

Right angles

Answer

Obtuse angles

Question 3

Find the perimeter of a triangle with sides measuring 3 cm, 4 cm, and 5 cm.

Accepted Answer

14 cm

Answer

6 cm

Answer

12 cm

Answer

24 cm

Question 4

In an equilateral triangle, what is true about its sides and angles?

Accepted Answer

All sides are equal and all angles are equal

Answer

All sides are equal, but angles may not be equal

Answer

All angles are equal, but sides may not be equal

Answer

Neither sides nor angles are necessarily equal

Question 5

The Pythagorean theorem states that in a right triangle, the area of the square on the hypotenuse is equal to:

Accepted Answer

The sum of the areas of the squares on the other two sides

Answer

The difference of the areas of the squares on the other two sides

Answer

The product of the areas of the squares on the other two sides

Answer

The quotient of the areas of the squares on the other two sides

Question 6

In a scalene triangle, which side can you determine to be the longest without knowing the exact measurements?

Accepted Answer

The side opposite the largest angle

Answer

The side opposite the smallest angle

Answer

The side perpendicular to the base

Answer

It cannot be determined without knowing exact measurements

Question 7

Which of the following is not a way to classify triangles based on side lengths?

Accepted Answer

Congruent

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 8

In an isosceles triangle with a base angle of 35 degrees, what is the measure of the vertex angle?

Accepted Answer

70 degrees

Answer

35 degrees

Answer

105 degrees

Answer

140 degrees

Question 9

A triangle with two equal sides and one right angle is specifically known as a:

Accepted Answer

Isosceles right triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Obtuse triangle

Question 10

In a right triangle, what trigonometric ratio relates the length of the opposite side to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 11

What is the sum of the interior angles in any triangle?

Accepted Answer

180 degrees

Answer

120 degrees

Answer

270 degrees

Answer

360 degrees

Question 12

What accurately characterizes a triangle?

Accepted Answer

A polygon with three sides whose angles sum up to 180 degrees

Answer

A polygon with three sides and two perpendicular angles

Answer

A polygon with three sides of equal length

Answer

A polygon with three sides and at least one wide angle

Question 13

Identify the triangle type with sides of equal length.

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 14

Which statement accurately describes the angles in a triangle?

Accepted Answer

The sum of its interior angles is 180 degrees

Answer

The sum of its exterior angles is 360 degrees

Answer

The sum of its interior angles is 90 degrees

Answer

The sum of its exterior angles is 180 degrees

Question 15

Identify a line segment connecting a vertex to the midpoint of the opposite side in a triangle.

Accepted Answer

A line segment connecting a vertex to the midpoint of the opposite side

Answer

A line segment connecting the midpoints of two sides

Answer

A line segment connecting a vertex to the midpoint of another side

Answer

A line segment parallel to one side and passing through the midpoint of another side

Question 16

Which figure is not a type of triangle?

Accepted Answer

Parallelogram

Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Question 17

A triangle with three equal sides is classified as a:

Accepted Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Right triangle

Question 18

Which theorem specifies that the Pythagorean theorem is only applicable to right triangles?

Accepted Answer

Converse of the Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Exterior Angle Theorem

Answer

Angle Bisector Theorem

Question 19

A triangle with one right angle is always considered:

Accepted Answer

Right

Answer

Acute

Answer

Obtuse

Answer

Equilateral

Question 20

Which set of side lengths could form a scalene triangle?

Accepted Answer

3 cm, 4 cm, 5 cm

Answer

6 cm, 6 cm, 6 cm

Answer

5 cm, 7 cm, 7 cm

Answer

10 cm, 5 cm, 10 cm

Question 21

The Triangle Inequality Theorem is represented by which inequality?

Accepted Answer

a + b > c

Answer

a + b < c

Answer

a - b < c

Answer

a - b > c

Question 22

In a right triangle, which side is always the longest?

Accepted Answer

Hypotenuse

Answer

Opposite side

Answer

Adjacent side

Answer

All sides are equal

Question 23

Which type of triangle has two equal sides?

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Answer

Right

Question 24

What is the name of the theorem that states the relationship between the sides of a triangle?

Accepted Answer

Triangle inequality theorem

Answer

Pythagorean theorem

Answer

Law of Sines

Answer

Law of Cosines

Question 25

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

Accepted Answer

Base x Height / 2

Answer

Length x Width

Answer

Pi x Radius^2

Answer

Perimeter x Height

Question 26

What is the theorem that states that two triangles are congruent if they have two pairs of equal sides?

Accepted Answer

Congruence theorem

Answer

Pythagorean theorem

Answer

Triangle inequality theorem

Answer

Converse of the isosceles triangle theorem

Question 27

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

Accepted Answer

It has three right angles

Answer

All sides are unequal

Answer

No two sides are equal

Answer

Its angles are all different

Question 28

In a triangle with angles labeled 60, 90, and x, what is the value of x?

Accepted Answer

30

Answer

60

Answer

90

Answer

120

Question 29

Which of the following is NOT a property of a right triangle?

Accepted Answer

It has three congruent sides

Answer

It has one right angle

Answer

It has two acute angles

Answer

The sum of its interior angles is 180 degrees

Question 30

Which of the following theorems states that the area of a triangle is equal to half the product of its base and height?

Accepted Answer

Triangle Area Formula

Answer

Triangle Inequality Theorem

Answer

Pythagorean Theorem

Answer

Law of Cosines

Question 31

A triangle with two congruent sides is called a:

Accepted Answer

isosceles triangle

Answer

scalene triangle

Answer

equilateral triangle

Answer

right triangle

Question 32

What is the area of a triangle with a base of 5 cm and a height of 7 cm?

Accepted Answer

17.5 cm²

Answer

12 cm²

Answer

35 cm²

Answer

50 cm²

Question 33

Which of the following statements about the exterior angle of a triangle is true?

Accepted Answer

It is equal to the sum of the opposite interior angles

Answer

It is less than the sum of the opposite interior angles

Answer

It is equal to the difference of the opposite interior angles

Answer

It is always greater than 180 degrees

Question 34

Which triangle has angles that measure 90°, 60°, and 30°?

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 35

Which theorem relates the squares of the legs and hypotenuse in a right triangle?

Accepted Answer

Pythagorean theorem

Answer

Triangle inequality theorem

Answer

Angle bisector theorem

Answer

Exterior angle theorem

Question 36

The sum of the interior angles of any triangle is:

Accepted Answer

180°

Answer

90°

Answer

270°

Answer

360°

Question 37

Which of the following is not a criterion for triangle similarity?

Accepted Answer

RHS (Right-Angle-Hypotenuse-Angle)

Answer

SSS (Side-Side-Side)

Answer

SAS (Side-Angle-Side)

Answer

ASA (Angle-Side-Angle)

Question 38

A median of a triangle connects a vertex to the:

Accepted Answer

Midpoint of the opposite side

Answer

Circumcenter of the triangle

Answer

Orthocenter of the triangle

Answer

Incenter of the triangle

Question 39

The area of a triangle can be calculated using the formula:

Accepted Answer

½ * base * height

Answer

π * radius²

Answer

s(s-a)(s-b)(s-c)

Answer

a² + b² - c²

Question 40

In a triangle, the side opposite the largest angle is the:

Accepted Answer

Longest side

Answer

Shortest side

Answer

Middle side

Answer

Equal to the other sides

Question 41

An obtuse triangle contains an angle that measures:

Accepted Answer

Greater than 90°

Answer

Less than 90°

Answer

Exactly 90°

Answer

Exactly 180°

Question 42

Which statement about a right triangle is incorrect?

Accepted Answer

All sides of a right triangle are of equal length

Answer

One of the angles in a right triangle is always 90 degrees

Answer

The sum of the angles of a right triangle is 180 degrees

Answer

The Pythagorean theorem applies to right triangles

Question 43

A triangle with angles measuring 60, 90, and 30 degrees is classified as:

Accepted Answer

Right and isosceles

Answer

Equilateral and scalene

Answer

Acute and equilateral

Answer

Obtuse and scalene

Question 44

What is the formula for calculating the area of a triangle with base 'b' and height 'h'?

Accepted Answer

1/2 * b * h

Answer

1/4 * b * h

Answer

2 * b * h

Answer

b * h

Question 45

Which theorem states that an angle bisector divides the opposite side of a triangle into segments that are proportional to the lengths of the adjacent sides?

Accepted Answer

Angle Bisector Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Converse of the Pythagorean Theorem

Question 46

In a triangle, the perpendicular line segment drawn from a vertex to the opposite side is called the:

Accepted Answer

Altitude

Answer

Angle bisector

Answer

Median

Answer

Hypotenuse

Question 47

The point where the three medians of a triangle intersect is called the:

Accepted Answer

Centroid

Answer

Orthocenter

Answer

Incenter

Answer

Circumcenter

Question 48

Which of the following is a property of a triangle?

Accepted Answer

The sum of its interior angles is 180 degrees.

Answer

It has a 90-degree angle.

Answer

It has four sides.

Answer

All three sides are equal.

Question 49

What is the name of the theorem that states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse?

Accepted Answer

Pythagorean theorem

Answer

Law of cosines

Answer

Law of sines

Answer

Triangle inequality theorem

Question 50

Which type of triangle has two equal sides?

Accepted Answer

Isosceles

Answer

Scalene

Answer

Right

Answer

Equilateral

Question 51

What is the name of the longest side of a triangle?

Accepted Answer

Hypotenuse

Answer

Altitude

Answer

Leg

Answer

Base

Question 52

Which of the following is a condition for a triangle to be valid?

Accepted Answer

The sum of the lengths of any two sides is greater than the length of the third side.

Answer

All three sides are equal.

Answer

It has three right angles.

Question 53

What is the name of the line segment that connects a vertex of a triangle to the midpoint of the opposite side?

Accepted Answer

Median

Answer

Altitude

Answer

Orthocenter

Answer

Angle bisector

Question 54

Which transformation is NOT a similarity transformation?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

Reflection