PM Review — Triangles

Question 1 Difficulty 1

Draw a triangle and label it as a triangle.

A A circle
B A triangle
C A square
D A rectangle

💡 Explanation You should have drawn a triangle and labeled it correctly.

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

Draw an equilateral triangle.

A All sides are different
B All sides are equal
C Two sides are equal
D No sides are equal

💡 Explanation An equilateral triangle has all sides 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 3 Difficulty 1

Draw an isosceles triangle.

A All sides are equal
B Two sides are equal
C No sides are equal
D All angles are 90 degrees

💡 Explanation An isosceles triangle has two sides that are 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 4 Difficulty 1

Draw a scalene triangle.

A All sides are equal
B Two sides are equal
C All sides are different
D One angle is 90 degrees

💡 Explanation A scalene triangle has all 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 5 Difficulty 1

Draw a triangle and label its three angles as A, B, and C.

A A triangle has four angles
B Angles can be any measure
C A triangle has three angles
D Angles can only be acute

💡 Explanation A triangle always has three angles.

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

Draw an equilateral triangle and label each angle.

A Each angle is 60 degrees
B Each angle is 45 degrees
C Each angle is 90 degrees
D Angles vary

💡 Explanation In an equilateral triangle, each angle measures 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 7 Difficulty 1

Draw a triangle and mark its sides as A, B, and C.

A A triangle has two sides
B A triangle has three sides
C A triangle has four sides
D A triangle has one side

💡 Explanation A triangle has three sides.

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

Draw a triangle and label it as 'Triangle ABC'.

A Triangle has two vertices
B Triangle has three vertices
C Triangle has four vertices
D Triangle has one vertex

💡 Explanation A triangle has 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 9 Difficulty 1

Draw a triangle and indicate that it is a polygon.

A A triangle is not a polygon
B A triangle is a polygon
C A triangle has four sides
D A triangle has five sides

💡 Explanation A triangle is indeed a polygon with three sides.

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

Draw a triangle and label it with a color.

A Triangles can't be colored
B Triangles can be any color
C All triangles are blue
D Triangles must be red

💡 Explanation Triangles can be drawn in any color.

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

Draw an isosceles triangle with sides 5 cm and 5 cm. What can be the length of the base?

A 3 cm
B 8 cm
C 6 cm
D 10 cm

💡 Explanation The length of the base can be 6 cm, satisfying the triangle inequality.

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

Draw a triangle with angles measuring 60°, 60°, and 60°. What type of triangle is this?

A Scalene
B Isosceles
C Equilateral
D Right

💡 Explanation This is an equilateral triangle with all angles 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 13 Difficulty 2

Draw a scalene triangle with sides 4 cm, 5 cm, and 6 cm. Verify if it can form a triangle.

A Yes
B No
C Not enough information
D Only two sides matter

💡 Explanation The sides satisfy the triangle inequality 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 14 Difficulty 2

Draw a triangle with side lengths 7 cm, 10 cm, and 3 cm. Can these lengths form a triangle?

A Yes
B No
C Maybe
D Only if angles are equal

💡 Explanation These lengths do not satisfy the triangle inequality 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 15 Difficulty 2

Draw a triangle with one angle measuring 90°. What type of triangle is this?

A Acutangle
B Obtuse
C Right
D Isosceles

💡 Explanation This is a right triangle because it has one 90° angle.

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

Draw an equilateral triangle with a perimeter of 18 cm. What is the length of each side?

A 4 cm
B 5 cm
C 6 cm
D 7 cm

💡 Explanation Each side of an equilateral triangle is equal, so 18 cm divided by 3 gives 6 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 17 Difficulty 2

Draw a triangle with angles 45°, 45°, and 90°. What is the type of triangle?

A Scalene
B Isosceles
C Equilateral
D Right

💡 Explanation This is a right triangle because it has one 90° angle.

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

Draw a triangle with sides measuring 8 cm, 6 cm, and 10 cm. Can these form a triangle?

A Yes
B No
C It depends
D Not enough information

💡 Explanation These lengths satisfy the triangle inequality 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 19 Difficulty 2

Draw a triangle with angles measuring 30°, 60°, and 90°. What is this triangle called?

A Scalene
B Right
C Isosceles
D Equilateral

💡 Explanation This is a right triangle because one angle measures 90°.

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

Draw a triangle with sides 12 cm, 16 cm, and 20 cm. Can these lengths form a triangle?

A Yes
B No
C Only if angles are equal
D Not enough information

💡 Explanation These lengths satisfy the triangle inequality 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 21 Difficulty 3

If a triangle has sides of length 3 cm, 4 cm, and x cm, which value of x will NOT form a triangle?

A 5 cm
B 6 cm
C 7 cm
D 8 cm

💡 Explanation For x = 8 cm, the sum of the other two sides is not greater than 8.

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

A triangle has two sides measuring 10 cm and 14 cm. What is the maximum possible length of the third side?

A 23 cm
B 24 cm
C 21 cm
D 22 cm

💡 Explanation The maximum length of the third side is less than the sum of the other two sides.

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

A triangle has angles measuring 70°, 50°, and x°. What is the value of x?

A 60°
B 70°
C 80°
D 90°

💡 Explanation The sum of angles in a triangle is 180°, so x = 180 - 70 - 50 = 60°.

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

If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the range of values for the third side?

A 6 to 16 cm
B 7 to 17 cm
C 8 to 20 cm
D 9 to 21 cm

💡 Explanation The third side must be greater than the difference and less than the sum of the other two.

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

A triangle has sides measuring 7 cm, 24 cm, and x cm. What value of x will form a triangle?

A 30 cm
B 20 cm
C 15 cm
D 10 cm

💡 Explanation x must be less than 31 cm and greater than 17 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 26 Difficulty 3

In a triangle with angles 40°, 70°, and x°, what is the value of x?

A 60°
B 50°
C 70°
D 80°

💡 Explanation The sum of the angles must equal 180°, hence x = 180 - 40 - 70 = 70°.

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

If a triangle has sides 8 cm, 15 cm, and x cm, what is the smallest integer value for x?

A 1 cm
B 3 cm
C 4 cm
D 5 cm

💡 Explanation The smallest integer for x must be greater than 7 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 28 Difficulty 3

A triangle has angles of 40°, 70°, and x°. What is the maximum possible value of x?

A 80°
B 70°
C 90°
D 100°

💡 Explanation x must be less than 70° to maintain the triangle condition.

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

In a triangle with sides measuring 11 cm, 14 cm, and x cm, which value of x will NOT form a triangle?

A 15 cm
B 20 cm
C 5 cm
D 10 cm

💡 Explanation x = 20 cm does not satisfy triangle inequality.

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

If the angles of a triangle are 80°, 60°, and x°, what is the value of x?

A 40°
B 50°
C 60°
D 70°

💡 Explanation The angles must sum up to 180°, thus x = 180 - 80 - 60 = 40°.

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

In a triangle with sides of lengths 5 cm, 12 cm, and x cm, find x when x is the longest side.

A 16 cm
B 15 cm
C 18 cm
D 17 cm

💡 Explanation The longest side must be less than the sum of the other two sides, so x < 17 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 32 Difficulty 4

A triangle has angles of 30°, 60°, and x°. Find the minimum value for x.

A 30°
B 60°
C 70°
D 90°

💡 Explanation To satisfy the triangle condition, x must be less than 90°.

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

If a triangle has sides 7 cm, 8 cm, and x cm, and x is the shortest side, what can be the maximum value of x?

A 10 cm
B 9 cm
C 6 cm
D 5 cm

💡 Explanation The shortest side must be less than the difference of the other two, so x < 9 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

A triangle has angles measuring 40°, 70°, and x°. What is the maximum value of x?

A 70°
B 80°
C 90°
D 100°

💡 Explanation x must be less than 70° to meet the triangle inequality.

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

For a triangle with sides measuring 10 cm, 24 cm, and x cm, find the maximum possible value of x.

A 34 cm
B 35 cm
C 36 cm
D 37 cm

💡 Explanation The longest side must be less than the sum of the other two sides, hence x < 34 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 36 Difficulty 4

If a triangle has angles 30°, 70°, and x°, find x when x is the smallest angle.

A 80°
B 60°
C 50°
D 40°

💡 Explanation The smallest angle must still satisfy the triangle condition, so x > 30°.

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

In a triangle with sides 6 cm, 10 cm, and x cm, what is the condition for x to be the longest side?

A x < 16 cm
B x < 15 cm
C x < 14 cm
D x < 13 cm

💡 Explanation For x to be the longest side, it must be less than the sum of the other two sides.

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

If a triangle has sides 10 cm, 24 cm, and x cm, where x is the shortest side, what is the maximum value of x?

A 10 cm
B 11 cm
C 12 cm
D 13 cm

💡 Explanation The shortest side must be less than the difference of the other two sides, so x < 11 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

A triangle has angles measuring 50°, 60°, and x°. Find the maximum possible value of x.

A 80°
B 70°
C 90°
D 100°

💡 Explanation x must be less than 70° to satisfy the triangle condition.

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

In a triangle with sides measuring 5 cm, 12 cm, and x cm, where x is the longest side, find the maximum value of x.

A 15 cm
B 16 cm
C 17 cm
D 14 cm

💡 Explanation For x to be the longest side, it must be less than the sum of the other two sides, so x < 17.

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?