Master Triangles: Conquer Geometry with Confidence

Question 1

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

Accepted Answer

24 cm²

Answer

12 cm²

Answer

48 cm²

Answer

96 cm²

Question 2

Which trigonometric function is related to the three sides of a triangle in the Law of Cosines?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cotangent

Question 3

Which theorem relates the exterior angle of a triangle to the opposite interior angles?

Accepted Answer

Exterior Angle Theorem

Answer

Angle Bisector Theorem

Answer

Triangle Inequality Theorem

Answer

Pythagorean Theorem

Question 4

Which type of similarity transformation increases the size of a figure?

Accepted Answer

Dilation

Answer

Rotation

Answer

Translation

Answer

Reflection

Question 5

Which type of triangle has all three sides of equal length?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 6

Which side of a right triangle is opposite the right angle and is the longest side?

Accepted Answer

Hypotenuse

Answer

Opposite side

Answer

Adjacent side

Answer

Leg

Question 7

In a triangle, what is the sum of its interior angles?

Accepted Answer

Equal to 180°

Answer

Less than 180°

Answer

Greater than 180°

Answer

Equal to 360°

Question 8

A triangle with two equal sides is classified as a:

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 9

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

Accepted Answer

A = (1/2) * b * h

Answer

A = (1/3) * b * h

Answer

A = b * h

Answer

A = (3/2) * b * h

Question 10

A triangle with congruent base angles is classified as a(n):

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 11

In a right triangle, the side opposite the right angle is known as the:

Accepted Answer

Opposite side

Answer

Adjacent side

Answer

Hypotenuse

Answer

Median

Question 12

In a triangle with two sides of equal length, the angles opposite those sides are:

Accepted Answer

Congruent

Answer

Supplementary

Answer

Equal to 90 degrees

Answer

Complementary

Question 13

The sum of the exterior angles of a triangle is:

Accepted Answer

360 degrees

Answer

180 degrees

Answer

270 degrees

Answer

540 degrees

Question 14

Find the measure of an exterior angle of a triangle with interior angles measuring 60, 70, and 50 degrees.

Accepted Answer

40 degrees

Answer

50 degrees

Answer

60 degrees

Answer

70 degrees

Question 15

Which theorem states that the sum of the squares of the lengths of any two sides of a triangle is equal to the square of the length of the third side?

Accepted Answer

Pythagorean Theorem

Answer

Sine Law

Answer

Cosine Law

Answer

Law of Sines

Question 16

Determine the measure of the greatest angle in a triangle with side lengths of 5 cm, 12 cm, and 13 cm.

Accepted Answer

120 degrees

Answer

45 degrees

Answer

60 degrees

Answer

90 degrees

Question 17

Which type of triangle has three congruent angles?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 18

In a triangle, the longest side is opposite to the ?

Accepted Answer

Largest angle

Answer

Smallest angle

Answer

Right angle

Answer

Obtuse angle

Question 19

The sum of the interior angles of a triangle is always equal to?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 20

If two sides of a triangle are congruent, then the triangle is classified as?

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Question 21

In the Pythagorean Theorem, a^2 + b^2 = c^2, c represents the?

Accepted Answer

Length of the hypotenuse

Answer

Length of a leg

Answer

Area of the triangle

Answer

Perimeter of the triangle

Question 22

Similar triangles have corresponding angles that are?

Accepted Answer

Congruent

Answer

Supplementary

Answer

Complementary

Answer

Equal in measure but not necessarily congruent

Question 23

The centroid of a triangle is the point where the?

Accepted Answer

Medians intersect

Answer

Altitudes intersect

Answer

Bisectors intersect

Answer

Perpendicular bisectors intersect

Question 24

If a triangle has two equal angles, then the triangle is classified as?

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Question 25

Which of the following is a defining property of isosceles triangles?

Accepted Answer

Exactly two sides are equal in length.

Answer

All three sides are equal in length.

Answer

Exactly one angle measures 90 degrees.

Answer

All of the angles measure less than 90 degrees.

Question 26

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

Accepted Answer

Equal to the sum of the squares of the other two sides.

Answer

Equal to the difference of the squares of the other two sides.

Answer

Equal to twice the sum of the squares of the other two sides.

Answer

Equal to half the sum of the squares of the other two sides.

Question 27

Which of the following is NOT a criterion for proving that two triangles are similar?

Accepted Answer

Equal perimeters

Answer

Equal side lengths

Answer

Equal angles

Answer

Congruent corresponding sides

Question 28

The point of intersection of the perpendicular bisectors of a triangle's sides is called the:

Accepted Answer

Orthocenter

Answer

Circumcenter

Answer

Incenter

Answer

Centroid

Question 29

The formula for calculating the area of a triangle is:

Accepted Answer

(1/2) * base * height

Answer

base + height

Answer

length * width

Answer

perimeter * height

Question 30

Which theorem can be used to prove that two triangles are congruent if their corresponding sides are proportional?

Accepted Answer

Triangle Congruence Theorem

Answer

Triangle Inequality Theorem

Answer

Pythagorean Theorem

Answer

Law of Cosines

Question 31

The segment drawn from a vertex of a triangle perpendicular to its opposite side is known as the:

Accepted Answer

Altitude

Answer

Median

Answer

Angle bisector

Answer

Centroid

Question 32

Which type of triangle has two equal sides?

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Answer

Obtuse

Question 33

In the triangle below, angle A measures 45 degrees and angle B measures 70 degrees. Find the measure of angle C:

Accepted Answer

65 degrees

Answer

70 degrees

Answer

75 degrees

Answer

80 degrees

Question 34

Calculate the perimeter of a triangle with sides of length 5 cm, 7 cm, and 9 cm:

Accepted Answer

21 cm

Answer

16 cm

Answer

25 cm

Answer

30 cm

Question 35

In a right triangle, what is the name of the side opposite the right angle?

Accepted Answer

Leg

Answer

Hypotenuse

Answer

Base

Answer

Altitude

Question 36

Find the area of a triangle with a base of 10 cm and a height of 6 cm.

Accepted Answer

30 cm²

Answer

16 cm²

Answer

60 cm²

Answer

10 cm²

Question 37

Which theorem relates the squares of the triangle's legs to the square of the hypotenuse?

Accepted Answer

Pythagorean Theorem

Answer

Sine Theorem

Answer

Cosine Theorem

Answer

Law of Sines

Question 38

Which condition is necessary for triangles to be congruent by the Side-Side-Side (SSS) Congruence Theorem?

Accepted Answer

Three pairs of corresponding sides are congruent.

Answer

Two pairs of corresponding sides and the included angle are congruent.

Answer

Two pairs of corresponding angles and the included side are congruent.

Answer

One pair of corresponding angles and two pairs of corresponding sides are congruent.

Question 39

In a triangle with side lengths of 5 cm, 7 cm, and 9 cm, which side is the longest?

Accepted Answer

9 cm

Answer

5 cm

Answer

7 cm

Answer

Cannot be determined from the given information

Question 40

A triangle with two congruent angles can be classified as a:

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Answer

Right

Question 41

The theorem used to calculate the length of the hypotenuse in a right triangle is the:

Accepted Answer

Pythagorean theorem

Answer

Triangle inequality theorem

Answer

Law of sines

Answer

Pythagorean conjecture

Question 42

The exterior angle inequality theorem states that:

Accepted Answer

The measure of an exterior angle of a triangle is greater than the measure of either non-adjacent interior angle.

Answer

The sum of the interior angles of a triangle is 180°.

Question 43

A triangle with all three sides congruent is known as a:

Accepted Answer

Equilateral

Answer

Right

Answer

Scalene

Answer

Isosceles

Question 44

The perimeter of a triangle with sides of length 'a', 'b', and 'c' is:

Accepted Answer

a + b + c

Answer

a^2 + b^2 + c^2

Answer

0.5 * (a + b + c)

Answer

2 * (a + b + c)

Question 45

Select the correct definition of the altitude of a triangle:

Accepted Answer

A line segment from a vertex perpendicular to the opposite side

Answer

A line segment bisecting an angle of a triangle

Answer

A line segment connecting two sides of a triangle

Question 46

In a triangle with sides of length 5, 12, and 13, the longest side has a length of:

Accepted Answer

13

Answer

12

Answer

5

Answer

All sides are equal

Question 47

Which characteristic is NOT always true of a triangle?

Accepted Answer

All sides are equal

Answer

The sum of the interior angles is 180 degrees

Answer

It has three sides

Answer

It has three angles

Question 48

In triangle ABC, angle A measures 30 degrees and angle B measures 60 degrees. What is the measure of angle C?

Accepted Answer

90 degrees

Answer

150 degrees

Answer

60 degrees

Answer

120 degrees

Question 49

If you know all three sides of triangle ABC have matching lengths to all three sides of triangle DEF, which theorem proves the triangles are congruent?

Accepted Answer

SSS (Side-Side-Side) Congruence Theorem

Answer

SAS (Side-Angle-Side) Congruence Theorem

Answer

ASA (Angle-Side-Angle) Congruence Theorem

Answer

AAS (Angle-Angle-Side) Congruence Theorem

Question 50

In a right triangle, the Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. What are the other two sides called?

Accepted Answer

Legs

Answer

Bases

Answer

Altitudes

Answer

Hypotenuses

Question 51

Which formula correctly calculates the area of a triangle?

Accepted Answer

1/2 * base * height

Answer

base * height

Answer

1/4 * base * height

Answer

base + height / 2

Question 52

Triangle ABC has a perimeter of 30 units. Side AB measures 10 units and side BC measures 12 units. What is the length of side AC?

Accepted Answer

8 units

Answer

18 units

Answer

10 units

Answer

22 units

Question 53

In triangle XYZ, XZ measures 10 cm and YZ measures 8 cm.  According to the Triangle Inequality Theorem, what is the possible range of lengths for side XY?

Accepted Answer

2 cm < XY < 18 cm

Answer

8 cm < XY < 10 cm

Answer

0 cm < XY < 18 cm

Answer

10 cm < XY < 18 cm

Question 54

Which of the following is NOT a classification of triangles by its sides and angles?

Accepted Answer

Obtuse Scalene

Answer

Equilateral Triangle

Answer

Isosceles Triangle

Answer

Right Triangle

Question 55

In triangle ABC, line segment AD is drawn from vertex A to the midpoint of side BC.  Line AD is called a median. What is always true about median AD?

Accepted Answer

AD divides BC into two segments of equal length

Answer

AD divides angle A into two angles of equal measure

Answer

AD is perpendicular to BC

Answer

AD is the longest side of triangle ABC

Question 56

You know the area and the base length of a triangle. Which formula helps you calculate the height of the triangle?

Accepted Answer

2 * area / base

Answer

area / 2 * base

Answer

base / area

Answer

area / base