Master Triangle Properties: Interactive Quizzes and Practice

Question 1

What is the defining property of all equilateral triangles?

Accepted Answer

Three congruent sides and three congruent angles

Answer

Two congruent sides and one right angle

Answer

Three congruent sides and two congruent angles

Question 2

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

Accepted Answer

All sides are equal in length.

Answer

The sum of the interior angles is 180 degrees.

Answer

One angle measures exactly 90 degrees.

Answer

The square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Question 3

Which congruence criterion can be used to prove that two triangles are congruent if they share two pairs of congruent angles?

Accepted Answer

ASA (Angle-Side-Angle)

Answer

AAS (Angle-Angle-Side)

Answer

SAS (Side-Angle-Side)

Answer

SS (Side-Side)

Question 4

Which of the following is NOT a theorem related to triangles?

Accepted Answer

Fermat's Last Theorem

Answer

Pythagorean Theorem

Answer

Incenter Theorem

Answer

Centroid Theorem

Question 5

Which property is **not** true for all triangles?

Accepted Answer

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle.

Answer

The sum of the interior angles is 180 degrees.

Answer

The exterior angle of a triangle is equal to the sum of the opposite interior angles.

Answer

The area of a triangle is equal to half the product of its base and height.

Question 6

Which theorem states that the sum of the interior angles of a triangle equals 180 degrees?

Accepted Answer

Triangle Angle Sum Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Law of Sines

Question 7

Which is NOT a criterion for triangle similarity?

Accepted Answer

SSA (Side-Side-Angle)

Answer

AAA (Angle-Angle-Angle)

Answer

SSS (Side-Side-Side)

Answer

SAS (Side-Angle-Side)

Question 8

In triangle ABC, if AB = AC and BC = 10, then angle BAC measures:

Accepted Answer

60 degrees

Answer

30 degrees

Answer

45 degrees

Answer

90 degrees

Question 9

Which theorem relates the ratios of the sides of similar triangles?

Accepted Answer

Triangle Proportionality Theorem

Answer

Theorem of Thales

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Question 10

In triangle PQR, if angle PQR = 90 degrees and PQ = 6, then the length of QR is:

Accepted Answer

6√2

Answer

√5

Answer

6

Answer

12

Question 11

An exterior angle of a triangle is formed by:

Accepted Answer

A side and an extended side

Answer

Two adjacent sides

Answer

Two non-adjacent sides

Answer

Two medians

Question 12

Which of the following is NOT a property of congruent triangles?

Accepted Answer

Equal medians

Answer

Equal side lengths

Answer

Equal angles

Answer

Equal heights

Question 13

In a triangle with sides a, b, and c, the angle opposite side c is known as:

Accepted Answer

Angle C

Answer

Angle A

Answer

Angle B

Answer

Angle D

Question 14

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 15

Which of the following is the equation for the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b

Answer

b² + c² = a

Question 16

In a triangle, the segment connecting the midpoint of two sides is called a:

Accepted Answer

Median

Answer

Altitude

Answer

Base

Answer

Bisector

Question 17

Which of the following is NOT a condition for two triangles to be congruent by the Angle-Angle-Side (AAS) theorem?

Accepted Answer

The triangles have equal areas.

Answer

Two angles and one side are congruent.

Answer

The included side is opposite the congruent angles.

Answer

The third angle is congruent.

Question 18

Which properties are true for congruent triangles?

Accepted Answer

Equal side lengths, equal angles, and equal areas

Answer

Equal side lengths and equal angles

Answer

Equal angles and equal areas

Answer

Equal side lengths and equal areas

Question 19

If a triangle has two angles measuring 60 degrees, what is the measure of the third angle?

Accepted Answer

120 degrees

Answer

30 degrees

Answer

60 degrees

Answer

90 degrees

Question 20

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

Accepted Answer

A = 1/2 * base * height

Answer

A = base * height

Answer

A = (1/2) * base * (height^2)

Answer

A = (1/4) * base * height

Question 21

What is the Pythagorean Theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

c^2 + b^2 = a^2

Answer

c^2 - a^2 = b^2

Question 22

What type of triangle has all sides of equal length?

Accepted Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Right triangle

Question 23

Which method is NOT used to prove triangles congruent?

Accepted Answer

Angle-Angle-Angle (AAA)

Answer

Side-Side-Side (SSS)

Answer

Angle-Side-Angle (ASA)

Answer

Side-Angle-Side (SAS)

Question 24

Calculate the area of a triangle with a 6 cm base and an 8 cm height.

Accepted Answer

24 cm²

Answer

12 cm²

Answer

48 cm²

Answer

96 cm²

Question 25

Which method can be used to prove the Triangle Inequality Theorem?

Accepted Answer

Proof by contradiction

Answer

Using the Pythagorean Theorem

Answer

Using similar triangles

Question 26

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

120 degrees

Answer

270 degrees

Question 27

Which theorem relates the length of a triangle's median to its side lengths?

Accepted Answer

Median Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Altitude Theorem

Question 28

Which of the following is NOT a criterion used to establish the congruence of two triangles?

Accepted Answer

Angle-Angle-Angle (AAA)

Answer

Side-Side-Side (SSS)

Answer

Side-Angle-Side (SAS)

Answer

Hypotenuse-Leg (HL)

Question 29

What theorem establishes the relationship between the areas of two similar triangles?

Accepted Answer

Triangle Area Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Law of Sines

Question 30

In a right triangle, which formula represents the relationship between the squares of the lengths of its sides?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

b² - c² = a²

Question 31

Which expression calculates the area of a triangle?

Accepted Answer

1/2 * base * height

Answer

base + height

Answer

side1 * side2 * side3

Answer

perimeter / 2

Question 32

Which type of right triangle has angles measuring 30, 60, and 90 degrees?

Accepted Answer

30-60-90 triangle

Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Question 33

In a 30-60-90 triangle, how does the length of the hypotenuse compare to the length of the shorter leg?

Accepted Answer

Twice as long

Answer

Three times as long

Answer

Four times as long

Answer

Equal in length

Question 34

Which theorem establishes that the sum of the measures of the interior angles of any triangle is equal to 180 degrees?

Accepted Answer

Triangle Sum Theorem

Answer

Theorem of Congruence

Answer

Pythagorean Theorem

Answer

Theorem of Similarity

Question 35

Triangles having the same shape but not necessarily the same size are referred to as:

Accepted Answer

Similar triangles

Answer

Equilateral triangles

Answer

Congruent triangles

Answer

Isosceles triangles

Question 36

A triangle with two sides of equal length is known as a:

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Asymmetric triangle

Answer

Scalene triangle

Question 37

The formula to calculate the area of a triangle is:

Accepted Answer

Area = (1/2) * base * height

Answer

Area = length * width

Answer

Area = circumference * radius

Answer

Area = perimeter * base

Question 38

The sum of the exterior angles of any triangle measures:

Accepted Answer

360 degrees

Answer

270 degrees

Answer

90 degrees

Answer

180 degrees

Question 39

Which of the following is NOT a property of all triangles?

Accepted Answer

All sides are equal.

Answer

Opposite sides are equal to opposite angles.

Answer

The sum of the interior angles is 180 degrees.

Answer

The angle opposite the longest side is the largest.

Question 40

If the scale factor between two similar triangles is 2, what is the ratio of their areas?

Accepted Answer

4:1

Answer

1:4

Answer

2:1

Question 41

Which of the following is a type of equilateral triangle?

Accepted Answer

Regular triangle

Answer

Scalene triangle

Answer

Isosceles triangle

Answer

Right triangle

Question 42

Which property is **not** true for congruent triangles?

Accepted Answer

Corresponding angles are supplementary.

Answer

Corresponding angles are congruent in measure.

Answer

The triangles have the same shape and size.

Answer

Corresponding sides are equal in length.

Question 43

Two similar triangles have corresponding sides with a ratio of 2:3. If the smaller triangle has a side length of 8 cm, what is the corresponding side length of the larger triangle?

Accepted Answer

12 cm

Answer

4 cm

Answer

16 cm

Answer

6 cm

Question 44

Triangle ABC is isosceles with AB = AC. If ∠B measures 55 degrees, what is the measure of ∠A?

Accepted Answer

70 degrees

Answer

125 degrees

Answer

110 degrees

Answer

55 degrees

Question 45

Triangle ABC is similar to triangle DEF. If AB = 6 cm, DE = 9 cm, and BC = 8 cm, what is the length of EF?

Accepted Answer

12 cm

Answer

4 cm

Answer

16 cm

Answer

8 cm

Question 46

A triangle has angles measuring 45°, 60°, and 75°. What type of triangle is it?

Accepted Answer

Scalene

Answer

Right

Answer

Isosceles

Answer

Equilateral

Question 47

Which statement is true for all triangles?

Accepted Answer

The sum of the interior angles is 180 degrees.

Answer

Pythagorean's theorem applies.

Answer

The longest side is always opposite the largest angle.

Answer

The area is equal to half the base times the height.

Question 48

Consider two triangles with side lengths a, b, c and x, y, z respectively. Which condition implies that the triangles are congruent by the Side-Side-Side (SSS) Congruence Theorem?

Accepted Answer

a = x, b = y, c = z

Answer

a² + b² = c²

Answer

a + b > x + y

Answer

∠A = ∠X, ∠B = ∠Y

Question 49

Which statement about similar triangles is incorrect?

Accepted Answer

Corresponding sides are proportional, but angles are not congruent.

Answer

Corresponding angles are congruent.

Answer

Ratios of corresponding sides are equal.

Question 50

In a right triangle with legs of length 3 cm and 4 cm, what is the length of the hypotenuse?

Accepted Answer

5 cm

Answer

6 cm

Answer

7 cm

Answer

8 cm

Question 51

Which type of triangle has three equal sides?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 52

Consider a triangle with vertices A(-3, 2), B(1, 4), and C(5, 0). What is the length of the side opposite angle B?

Accepted Answer

√52

Answer

√29

Answer

√20

Question 53

Which theorem can be used to prove that two triangles are similar, even if they do not have any congruent sides?

Accepted Answer

Angle-Angle-Side (AAS) Similarity Theorem

Answer

Side-Side-Side (SSS) Congruence Theorem

Answer

Angle-Side-Angle (ASA) Congruence Theorem

Answer

Hypotenuse-Leg (HL) Congruence Theorem

Question 54

If the perimeter of a triangle is 30 cm and the lengths of two of its sides are 10 cm and 12 cm, what is the length of the third side?

Accepted Answer

8 cm

Answer

9 cm

Answer

10 cm

Answer

7 cm

Question 55

Which of the following is a valid proof that a triangle is isosceles?

Accepted Answer

If two angles of a triangle are congruent, then the opposite sides are congruent.

Answer

If the diagonals of a parallelogram bisect each other, then the parallelogram is a rectangle.

Answer

If the product of two numbers is even, then both numbers must be even.