PM Review — Triangles

Question 1 Difficulty 1

What is a triangle?

A A three-sided polygon
B A four-sided polygon
C A five-sided polygon
D A two-sided polygon

💡 Explanation A triangle is defined as a three-sided polygon, which means it has three edges and three vertices.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 2 Difficulty 1

How many sides does an equilateral triangle have?

A One
B Two
C Three
D Four

💡 Explanation An equilateral triangle has three sides, all of which are equal in length.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 3 Difficulty 1

What type of triangle has two equal sides?

A Scalene Triangle
B Isosceles Triangle
C Equilateral Triangle
D Right Triangle

💡 Explanation An isosceles triangle is defined as a triangle with at least two sides that are equal in length.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 4 Difficulty 1

What is the sum of the angles in any triangle?

A 90 degrees
B 180 degrees
C 360 degrees
D 270 degrees

💡 Explanation The sum of the angles in any triangle is always 180 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 5 Difficulty 1

Which triangle has all sides of different lengths?

A Equilateral Triangle
B Isosceles Triangle
C Scalene Triangle
D Right Triangle

💡 Explanation A scalene triangle is defined by having all three sides of different lengths.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 6 Difficulty 1

If a triangle has angles of 60 degrees, 60 degrees, and 60 degrees, what type is it?

A Isosceles Triangle
B Scalene Triangle
C Equilateral Triangle
D Right Triangle

💡 Explanation A triangle with all angles equal to 60 degrees is called an equilateral triangle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 7 Difficulty 1

Which of the following is NOT a type of triangle?

A Equilateral
B Isosceles
C Quadrilateral
D Scalene

💡 Explanation A quadrilateral is a four-sided figure, while equilateral, isosceles, and scalene are types of triangles.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 8 Difficulty 1

What is the name of a triangle with one angle greater than 90 degrees?

A Acute Triangle
B Right Triangle
C Obtuse Triangle
D Equilateral Triangle

💡 Explanation A triangle with one angle greater than 90 degrees is called an obtuse triangle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 9 Difficulty 1

In an isosceles triangle, the angles opposite the equal sides are:

A Different
B Equal
C Greater
D Less

💡 Explanation In an isosceles triangle, the angles opposite the equal sides are always equal.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 10 Difficulty 1

Which of the following triangles can be formed with sides of lengths 3 cm, 4 cm, and 5 cm?

A Equilateral
B Isosceles
C Scalene
D None

💡 Explanation A triangle with sides of lengths 3 cm, 4 cm, and 5 cm is a scalene triangle, as all sides are of different lengths.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 11 Difficulty 2

If two angles of a triangle are 45 degrees and 55 degrees, what is the third angle?

A 90 degrees
B 100 degrees
C 80 degrees
D 70 degrees

💡 Explanation The third angle can be found by subtracting the sum of the known angles from 180 degrees: 180 - (45 + 55) = 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 12 Difficulty 2

A triangle has sides of lengths 8 cm, 8 cm, and 5 cm. What type of triangle is it?

A Equilateral
B Isosceles
C Scalene
D Right

💡 Explanation The triangle has two equal sides, which makes it an isosceles triangle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 13 Difficulty 2

What is the perimeter of a triangle with sides 7 cm, 3 cm, and 5 cm?

A 15 cm
B 25 cm
C 10 cm
D 20 cm

💡 Explanation The perimeter is calculated by adding all sides: 7 + 3 + 5 = 15 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 14 Difficulty 2

In a triangle, one angle is 90 degrees, and the other angles are 30 degrees and ___ degrees. What is the missing angle?

A 60 degrees
B 45 degrees
C 75 degrees
D 80 degrees

💡 Explanation The angles in a triangle add up to 180 degrees. The missing angle is 180 - (90 + 30) = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 15 Difficulty 2

A triangle has sides of lengths 10 cm, 10 cm, and 12 cm. What is the type of triangle?

A Equilateral
B Isosceles
C Scalene
D Right

💡 Explanation The triangle has two equal sides (10 cm), making it an isosceles triangle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 16 Difficulty 2

What is the area of a triangle with a base of 10 cm and height of 5 cm?

A 25 cm²
B 50 cm²
C 15 cm²
D 30 cm²

💡 Explanation The area of a triangle is calculated using the formula: (1/2) * base * height = (1/2) * 10 * 5 = 25 cm².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 17 Difficulty 2

A triangle has angles measuring 70 degrees and 40 degrees. What is the type of triangle based on its angles?

A Acute Triangle
B Obtuse Triangle
C Right Triangle
D Scalene Triangle

💡 Explanation Since all angles are less than 90 degrees, the triangle is classified as an acute triangle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 18 Difficulty 2

If one angle of a triangle is 60 degrees and the other two angles are equal, what is the measure of each of the equal angles?

A 60 degrees
B 70 degrees
C 90 degrees
D 80 degrees

💡 Explanation Let the equal angles be x. Then, 60 + 2x = 180. Thus, 2x = 120, and x = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 19 Difficulty 2

A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. What type of triangle is it?

A Right Triangle
B Isosceles Triangle
C Scalene Triangle
D Obtuse Triangle

💡 Explanation This triangle is a right triangle as it follows the Pythagorean theorem: 5² + 12² = 13².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 20 Difficulty 2

What is the height of an equilateral triangle with a side of 6 cm?

A 3√3 cm
B 3 cm
C 6 cm
D 2√3 cm

💡 Explanation The height of an equilateral triangle can be calculated using the formula: height = (√3/2) * side = (√3/2) * 6 = 3√3 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 21 Difficulty 3

A triangle has sides of lengths 7 cm, 8 cm, and 9 cm. Calculate its semi-perimeter.

A 12 cm
B 14 cm
C 16 cm
D 18 cm

💡 Explanation The semi-perimeter is calculated as (7 + 8 + 9) / 2 = 24 / 2 = 12 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 22 Difficulty 3

If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

A 60 degrees
B 90 degrees
C 120 degrees
D 80 degrees

💡 Explanation Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180. Thus, 9x = 180, so x = 20. The largest angle is 4x = 80 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 23 Difficulty 3

In a triangle, one angle measures 50 degrees, and the second angle measures 70 degrees. Which type of triangle is it?

A Right Triangle
B Acute Triangle
C Obtuse Triangle
D Isosceles Triangle

💡 Explanation All angles are less than 90 degrees, making this triangle an acute triangle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 24 Difficulty 3

A triangle has one angle of 110 degrees. What can be said about the other two angles?

A Both are acute
B One is obtuse
C One is right
D They cannot exist

💡 Explanation The sum of all angles in a triangle must be 180 degrees. If one angle is 110 degrees, the other two cannot exist.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 25 Difficulty 3

If the lengths of the sides of a triangle are in the ratio 3:4:5, what type of triangle is it?

A Right Triangle
B Isosceles Triangle
C Acute Triangle
D Obtuse Triangle

💡 Explanation A triangle with sides in the ratio of 3:4:5 is a right triangle according to the Pythagorean theorem.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 26 Difficulty 3

A triangle has sides measuring 9 cm, 12 cm, and 15 cm. What is the area of this triangle?

A 54 cm²
B 72 cm²
C 36 cm²
D 45 cm²

💡 Explanation Using Heron's formula, area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter. Here, s = 18 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 27 Difficulty 3

A triangle has angles of 30 degrees and 60 degrees. What is the measure of the third angle?

A 90 degrees
B 60 degrees
C 70 degrees
D 80 degrees

💡 Explanation The third angle can be found by subtracting the sum of the known angles from 180 degrees: 180 - (30 + 60) = 90 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 28 Difficulty 3

In a triangle, if the lengths of two sides are 5 cm and 12 cm, what could be the length of the third side?

A 10 cm
B 7 cm
C 15 cm
D 20 cm

💡 Explanation The length of the third side must be less than the sum of the other two sides (5 + 12) and greater than their difference (12 - 5).

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 29 Difficulty 3

If the lengths of the sides of a triangle are 8 cm, 15 cm, and 17 cm, what type of triangle is it?

A Right Triangle
B Isosceles Triangle
C Scalene Triangle
D Acute Triangle

💡 Explanation This triangle is a right triangle because it satisfies the Pythagorean theorem: 8² + 15² = 17².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 30 Difficulty 3

A triangle has sides of 6 cm, 8 cm, and 10 cm. What is the semi-perimeter?

A 12 cm
B 14 cm
C 16 cm
D 18 cm

💡 Explanation The semi-perimeter is calculated as (6 + 8 + 10) / 2 = 24 / 2 = 12 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 31 Difficulty 4

A triangle has sides of lengths x, x, and 10. If x is the length of the equal sides, what is the minimum value of x so that a triangle can exist?

A 5
B 6
C 7
D 8

💡 Explanation For a triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side. Hence, 2x > 10, which gives x > 5.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 32 Difficulty 4

In triangle ABC, angle A is 40 degrees, and angle B is 60 degrees. What is angle C?

A 60 degrees
B 80 degrees
C 70 degrees
D 50 degrees

💡 Explanation The sum of angles in a triangle is 180 degrees. Thus, angle C = 180 - (40 + 60) = 80 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 33 Difficulty 4

A triangle has a perimeter of 30 cm, and the lengths of two sides are 12 cm and 8 cm. What is the length of the third side?

A 6 cm
B 10 cm
C 12 cm
D 4 cm

💡 Explanation The perimeter of a triangle is the sum of its sides: 30 = 12 + 8 + third side. So, the third side = 30 - 20 = 10 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 34 Difficulty 4

If a triangle has sides measuring 10 cm, 24 cm, and 26 cm, is it a right triangle?

A Yes
B No
C Cannot be determined
D Only if it is also isosceles

💡 Explanation This triangle satisfies the Pythagorean theorem: 10² + 24² = 26², confirming it is a right triangle.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 35 Difficulty 4

In triangle DEF, if angle D is 70 degrees and angle E is 50 degrees, what is angle F?

A 60 degrees
B 70 degrees
C 80 degrees
D 50 degrees

💡 Explanation The sum of angles in a triangle is 180 degrees. Angle F = 180 - (70 + 50) = 60 degrees.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 36 Difficulty 4

Given a triangle where the lengths of the sides are in the ratio 4:3:5, what type of triangle is it?

A Right Triangle
B Isosceles
C Scalene
D Acute

💡 Explanation A triangle with sides in the ratio of 4:3:5 is a right triangle based on the Pythagorean theorem.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 37 Difficulty 4

A triangle has an area of 24 cm² and a base of 6 cm. What is the height?

A 8 cm
B 6 cm
C 4 cm
D 10 cm

💡 Explanation The area of a triangle is given by the formula: Area = 1/2 * base * height. Thus, 24 = 1/2 * 6 * height, which gives height = 8 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 38 Difficulty 4

In triangle XYZ, if side XY is 10 cm, side XZ is 14 cm, and side YZ is 8 cm, what is the perimeter?

A 32 cm
B 28 cm
C 26 cm
D 30 cm

💡 Explanation The perimeter of a triangle is found by adding all sides: 10 + 14 + 8 = 32 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 39 Difficulty 4

If a triangle has a semi-perimeter of 20 cm and one side is 10 cm, what is the sum of the other two sides?

A 20 cm
B 30 cm
C 40 cm
D 50 cm

💡 Explanation The semi-perimeter is half the perimeter. Therefore, the total perimeter is 40 cm, and if one side is 10 cm, the sum of the other two sides is 40 - 10 = 30 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 40 Difficulty 4

A triangle has sides measuring 9 cm, 12 cm, and 15 cm. Is this triangle obtuse, acute, or right?

A Obtuse
B Acute
C Right
D Cannot be determined

💡 Explanation This triangle is a right triangle as it follows the Pythagorean theorem: 9² + 12² = 15².

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?