Classifying and Identifying Triangles

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1) A triangle with all angles less than 90 is classified as:

Explanation

All acute angles means an acute triangle.

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About This Quiz
Classifying And Identifying Triangles - Quiz

Are you ready to dive into the world of triangles? In this quiz, you’ll practice classifying triangles by both their sides and their angles — from equilateral to scalene, and from acute to right. You’ll explore questions that ask you to recognize valid triangles, calculate missing angles, and decide when... see morecertain measurements can or can’t form a triangle. Step by step, you’ll build confidence in identifying and understanding triangles, making geometry problems much easier to tackle! see less

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2) A triangle has angles of 80°, 50°, and 50°. Which type is it?

Explanation

The triangle has two equal angles (50° each) and one angle (80°) that is less than 90°. This makes it an isosceles triangle. Since all angles are less than 90°, it is classified as an acute triangle, thus it is an acute isosceles triangle.

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3) Which triangle has exactly one right angle and two equal sides?

Explanation

A right isosceles triangle is defined by having one right angle (90 degrees) and two sides that are equal in length.

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4) Which set of angles forms a valid triangle?

Explanation

For a set of angles to form a valid triangle, the sum of the angles must equal 180°. In option B, the angles sum to 90° + 45° + 45° = 180°, making it a valid triangle. The other options do not satisfy this condition.

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5) Which triangle can exist?

Explanation

Triangle inequality:


  • 5,5,10 fails (sum equals largest).

  • 7,8,15 fails (sum equals largest).

  • 9,9,5 works (each pair sums greater).

  • 2,2,5 fails (sum less than largest).


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6) A triangle with angles 90°, 30°, and 60° is:

Explanation

Right triangle with all angles different means Right scalene.

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7) A triangle has two angles that measure 45°. What is the measure of the third angle?

Explanation

In a triangle, the sum of the interior angles is always 180°. If two angles measure 45° each, their sum is 90°. Therefore, the third angle must be 180 - 90 = 90°.

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8) You are given two sides of 6 cm and 9 cm and the included angle of 50°. What can you conclude about the triangle?

Explanation

In the SSA (side-side-angle) condition ,When two sides and the included angle of a triangle are known, the triangle can be determined Unique triangle .

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9) If a triangle has sides 6 cm, 6 cm, and 6 cm, which statement is true?

Explanation

All equal sides means equilateral, which is always acute (all 60°)

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10) A triangle with three equal sides is called:

Explanation

A triangle with three equal sides is equilateral.

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11) If a triangle has angles 30°, 60°, and 90°, what type is it?

Explanation

Having a 90° angle makes it a right triangle.

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12) A triangle has sides 8 cm, 15 cm, and 17 cm. Which type of triangle is it?

Explanation

Check 82+152=64+225=289=172, so it’s right.

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13) A triangle has one angle measuring 120°. Which type of triangle is it?

Explanation

An angle greater than 90° makes it obtuse.

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14) You are given two sides of 10 cm and 7 cm and a nonincluded angle of 30° that is opposite the 7 cm side. What can you conclude about the triangle?

Explanation

In this scenario, given two sides and an angle opposite one of them, it can lead to the possibility of constructing two different triangles. This is known as the ambiguous case of the Law of Sines, where the smaller angle opposite the shorter side allows for more than one valid triangle configuration.

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15) A triangle with three unequal sides is called:

Explanation

Three different sides means scalene.

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16) You are given two sides of 10 cm and 7 cm and an acute angle that is opposite the 7 cm side, but the angle measure is not specified. What can you conclude about the triangle?

Explanation

The given dimensions and an unspecified angle indicate that there is insufficient information to determine the exact type of triangle that can be formed. The angle could allow for the possibility of multiple configurations of the triangle, hence 'Not enough information' is the correct conclusion.

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17) If a triangle has side lengths 10, 10, and 14, which type is it?

Explanation

The triangle has two sides of equal length (10 and 10), which classifies it as isosceles. Since the side lengths also satisfy the triangle inequality and the angle opposite the longest side (14) is less than 90 degrees, it is an isosceles acute triangle.

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18) Which of the following angle measures could not form a triangle?

Explanation

For three angles to form a triangle, their measures must sum up to exactly 180°. In option D, the angles are 100°, 40°, and 50°, which sum to 190° (100° + 40° + 50° = 190°). Since this exceeds 180°, these angles cannot form a triangle. The other options sum to 180° or less, making them valid combinations for triangle formation.

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19) You are given side lengths 4 cm, 7 cm, and 11 cm. What can you conclude about the triangle?

Explanation

Triangle inequality needs 4 + 7 > 11, but 4 + 7 = 11, so it no triangle.

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20) A triangle has sides of 7 cm, 7 cm, and 10 cm. Which type is it?

Explanation

Two equal sides means isosceles

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A triangle with all angles less than 90 is classified as:
A triangle has angles of 80°, 50°, and 50°. Which type is...
Which triangle has exactly one right angle and two equal sides?
Which set of angles forms a valid triangle?
Which triangle can exist?
A triangle with angles 90°, 30°, and 60° is:
A triangle has two angles that measure 45°. What is the measure of...
You are given two sides of 6 cm and 9 cm and the included angle of...
If a triangle has sides 6 cm, 6 cm, and 6 cm, which statement is true?
A triangle with three equal sides is called:
If a triangle has angles 30°, 60°, and 90°, what type is...
A triangle has sides 8 cm, 15 cm, and 17 cm. Which type of triangle is...
A triangle has one angle measuring 120°. Which type of triangle is...
You are given two sides of 10 cm and 7 cm and a nonincluded angle of...
A triangle with three unequal sides is called:
You are given two sides of 10 cm and 7 cm and an acute angle that is...
If a triangle has side lengths 10, 10, and 14, which type is it?
Which of the following angle measures could not form a triangle?
You are given side lengths 4 cm, 7 cm, and 11 cm. What can you...
A triangle has sides of 7 cm, 7 cm, and 10 cm. Which type is it?
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