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Quizzes > High School Quizzes > Mathematics

Practice Quiz: Classifying Triangles Worksheet

Master triangle classification with engaging practice tasks

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Colorful paper art promoting Triangle Type Challenge quiz for middle school geometry students.

Which triangle has all three sides of equal length?
Isosceles triangle
Equilateral triangle
Right triangle
Scalene triangle
An equilateral triangle has all three sides equal, and consequently, all three angles are equal (each being 60°). This is the defining property of an equilateral triangle.
Which triangle has exactly two sides of equal length?
Scalene triangle
Equilateral triangle
Isosceles triangle
Right triangle
An isosceles triangle is characterized by having exactly two sides of equal length. This also means that the base angles are equal in measure.
Which triangle has no sides of equal length?
Equilateral triangle
Scalene triangle
Isosceles triangle
Right triangle
A scalene triangle has all sides of different lengths, which implies that none of its angles are equal. This distinguishes it from both equilateral and isosceles triangles.
Which triangle has one angle that measures 90°?
Obtuse triangle
Acute triangle
Equilateral triangle
Right triangle
A right triangle is defined by the presence of one 90° angle. The remaining angles in a right triangle are acute, ensuring the total sum is 180°.
Which triangle has all interior angles measuring less than 90°?
Right triangle
Obtuse triangle
Isosceles triangle
Acute triangle
An acute triangle is one in which all interior angles are less than 90°. This property sets it apart from right triangles and obtuse triangles.
What is the sum of the interior angles in any triangle?
180°
270°
90°
360°
The sum of the interior angles in any triangle is always 180°. This fundamental property is used to solve many problems involving triangles.
If a triangle has one angle measuring 90° and the other two angles measuring less than 90°, what type of triangle is it?
Obtuse triangle
Equilateral triangle
Acute triangle
Right triangle
A triangle with one 90° angle is classified as a right triangle. The other two angles must be acute to complete the 180° total.
What type of triangle has one angle that is greater than 90°?
Acute triangle
Obtuse triangle
Isosceles triangle
Right triangle
An obtuse triangle has one angle that exceeds 90°. This distinct characteristic differentiates it from acute and right triangles.
In an isosceles triangle, if the vertex angle measures 40°, what is the measure of each base angle?
70°
80°
60°
40°
The sum of the angles in any triangle is 180°. Subtracting the vertex angle (40°) and dividing the remaining 140° equally between the two base angles gives 70° each.
Which triangle type can be classified by both its sides and its angles if all sides and angles are congruent?
Equilateral triangle
Right triangle
Scalene triangle
Isosceles triangle
An equilateral triangle has all sides equal and all angles equal (each measuring 60°). This dual characteristic makes it unique among triangles.
A triangle has side lengths of 5 cm, 5 cm, and 8 cm. What type of triangle is it?
Right triangle
Scalene triangle
Isosceles triangle
Equilateral triangle
Since two sides are of equal length (5 cm each), the triangle is an isosceles triangle. The unequal third side confirms it is not equilateral.
In a right triangle, which theorem is used to calculate an unknown side length?
Law of Sines
Isosceles triangle theorem
Triangle sum theorem
Pythagorean theorem
The Pythagorean theorem is specifically used in right triangles to relate the lengths of the sides. It states that the square of the hypotenuse equals the sum of the squares of the other two sides.
What is the minimum requirement for the measure of any interior angle in a non-degenerate triangle?
Greater than 0°
Exactly 30°
Exactly 60°
0°
Every interior angle in a non-degenerate triangle must be greater than 0°, as a 0° angle would imply that the triangle's points are collinear. This is a fundamental principle of triangle geometry.
Which triangle has a right angle and two congruent sides?
Right isosceles triangle
Acute triangle
Scalene triangle
Equilateral triangle
A right isosceles triangle features a 90° angle along with two congruent sides. This blend of properties distinctly identifies it from other triangle types.
What is the measure of each interior angle in an equilateral triangle?
60°
90°
45°
120°
Since all interior angles of a triangle add up to 180°, an equilateral triangle, having three equal angles, will have each angle measuring 60°. This property is inherent to equilateral triangles.
Given a triangle with side lengths 7 cm, 24 cm, and 25 cm, classify the triangle by its sides and angles.
Scalene right triangle
Equilateral triangle
Scalene obtuse triangle
Isosceles right triangle
The side lengths 7, 24, and 25 cm satisfy the Pythagorean theorem, confirming the presence of a 90° angle. Additionally, as all sides differ in length, the triangle is classified as scalene.
A triangle with angles measuring 40°, 40°, and 100° is best classified as:
Scalene obtuse triangle
Isosceles obtuse triangle
Equilateral triangle
Isosceles acute triangle
The triangle has two equal angles (40° each), making it isosceles. With one angle measuring 100° (which is greater than 90°), it is also an obtuse triangle.
A triangle with side lengths in the proportion 3:4:5 is an example of which type of triangle?
Scalene right triangle
Isosceles triangle
Right isosceles triangle
Obtuse triangle
The 3:4:5 ratio corresponds to a well-known Pythagorean triple, indicating a right angle. Since all three sides have different lengths, the triangle is scalene.
A triangle has two sides of equal length and one angle measuring 120°. How would you classify this triangle?
Isosceles acute triangle
Equilateral triangle
Scalene obtuse triangle
Isosceles obtuse triangle
With two equal sides, the triangle is isosceles. The 120° angle, being greater than 90°, classifies it as obtuse, making the triangle an isosceles obtuse triangle.
A triangle has interior angles in the ratio 2:3:4. What are the measures of its angles?
40°, 60°, 80°
30°, 60°, 90°
45°, 60°, 75°
20°, 60°, 100°
The ratio 2:3:4 indicates the angles can be expressed as 2x, 3x, and 4x. Since 2x + 3x + 4x = 9x equals 180°, x equals 20°, yielding angles of 40°, 60°, and 80°.
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Study Outcomes

  1. Analyze the characteristics of triangles based on side lengths and angle measures.
  2. Identify different triangle types using geometric definitions.
  3. Apply triangle classification concepts to solve practice problems.
  4. Evaluate the properties of triangles to determine the appropriate category.
  5. Reinforce understanding of fundamental geometric concepts in preparation for exams.

Classifying Triangles Worksheet Cheat Sheet

  1. Equilateral Triangles - These triangles have all sides and angles equal, each measuring 60°, giving them perfect symmetry and balance. Students often spot them in tiling patterns and architecture because of their uniformity and aesthetic appeal. Equilateral Triangle - Wikipedia
  2. Isosceles Triangles - Featuring two equal sides and two equal base angles, these triangles are the go‑to example for symmetry in proofs. They show up everywhere from bridge designs to spotlight beams. Types of Triangles - BYJU'S
  3. Scalene Triangles - With all sides and angles different, scalene triangles are the VIPs of variety in geometry. They teach you how to tackle non‑symmetrical shapes and sharpen problem‑solving skills. Types of Triangles - Math.net
  4. Acute Triangles - Every interior angle is less than 90°, giving these triangles a pointy, compact look. Spotting them quickly helps you breeze through angle‑chasing puzzles. Acute and Obtuse Triangles - Wikipedia
  5. Obtuse Triangles - One angle exceeds 90°, making the shape look stretched or leaning back. These triangles pop up in real‑world scenarios like ramp designs and survey maps. Acute and Obtuse Triangles - Wikipedia
  6. Right Triangles - Defined by a perfect 90° angle, right triangles are the heart of trigonometry and give us the Pythagorean theorem. From ladders to GPS tech, they're everywhere! Right Triangle - Wikipedia
  7. Pythagorean Theorem - In any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². This rule unlocks distance and area calculations in science and engineering. Types of Triangles - Math.net
  8. Triangle Angle Sum Property - No matter the shape, a triangle's interior angles always add up to 180°. Mastering this lets you solve for missing angles in a snap! Types of Triangles - BYJU'S
  9. Triangle Inequality Theorem - The sum of the lengths of any two sides must exceed the third side. Think of it as the "must‑have strength" rule for triangle construction. Types of Triangles - Math.net
  10. Classifying Triangles by Sides and Angles - Combine side‑based and angle‑based names (like "right isosceles") to get a full picture. This toolkit helps you quickly identify and solve geometry problems with flair. Types of Triangles - BYJU'S
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