# Geometry ---- Classifying Triangles 10/17/09

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Write the letter for the correct term beside each triangle description.

• 1.

### Sides lengths are 3cm, 4cm, and 6cm.

• A.

Right

• B.

Obtuse

• C.

Acute

• D.

Scalene

• E.

Isosceles

D. Scalene
Explanation
The given triangle has sides of lengths 3cm, 4cm, and 6cm. A scalene triangle is a triangle in which all three sides have different lengths. Since the sides of this triangle have different lengths, it can be classified as a scalene triangle.

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• 2.

### Angle measures are 40*, 60*, and 80*.

• A.

Right

• B.

Obtuse

• C.

Acute

• D.

Scalene

• E.

Isosceles

C. Acute
Explanation
The given angle measures of 40°, 60°, and 80° are all less than 90°, which classifies them as acute angles. Acute angles are angles that are less than 90°. Therefore, the correct answer is "acute".

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• 3.

### Angle measures are 25*, 10*, and 145*.

• A.

Right

• B.

Obtuse

• C.

Acute

• D.

Scalene

• E.

Isosceles

B. Obtuse
Explanation
The given angle measures are 25°, 10°, and 145°. An obtuse angle is any angle that measures greater than 90° but less than 180°. Since the measure of the largest angle (145°) is greater than 90°, it is an obtuse angle. Therefore, the answer is obtuse.

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• 4.

### Side measures are 6in, 5in, and 6in.

• A.

Right

• B.

Obtuse

• C.

Acute

• D.

Scalene

• E.

Isosceles

E. Isosceles
Explanation
The given side measures of 6in, 5in, and 6in indicate that two sides have the same length, making it an isosceles triangle. An isosceles triangle has at least two sides of equal length.

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• 5.

### Angle measures are 30*, 60*, and 90*.

• A.

Right

• B.

Obtuse

• C.

Acute

• D.

Scalene

• E.

Isosceles

A. Right
Explanation
The given angle measures of 30°, 60°, and 90° indicate that one of the angles is a right angle, which measures 90°. A right angle is formed when two lines intersect and create a 90° angle, forming an "L" shape. Therefore, the correct answer is "right."

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• 6.

### A triangle _________________ has a right angle and an obtuse angle.

• A.

Sometimes

• B.

Always

• C.

Never

C. Never
Explanation
A triangle can never have both a right angle and an obtuse angle at the same time. In a right-angled triangle, one angle measures exactly 90 degrees, while in an obtuse-angled triangle, one angle measures more than 90 degrees. Since these two angles are mutually exclusive, it is not possible for a triangle to simultaneously have both a right angle and an obtuse angle. Therefore, the correct answer is "never."

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• 7.

### The acute angles of a right triangle are ___________ complementary.

• A.

Sometimes

• B.

Always

• C.

Never

B. Always
Explanation
In a right triangle, one of the angles is always 90 degrees. The sum of the measures of the other two angles must be 90 degrees in order for the triangle to be a right triangle. Therefore, the acute angles of a right triangle are always complementary, meaning they add up to 90 degrees.

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• 8.

### An obtuse triangle is ___________ an isosceles triangle.

• A.

Sometimes

• B.

Always

• C.

Never

A. Sometimes
Explanation
An obtuse triangle is sometimes an isosceles triangle because an obtuse triangle can have two equal sides, which would make it isosceles. However, not all obtuse triangles are isosceles because they can also have three unequal sides. Therefore, the statement "An obtuse triangle is sometimes an isosceles triangle" is correct.

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• 9.

### An isosceles triangle is ____________ an equilateral triangle.

• A.

Sometimes

• B.

Always

• C.

Never

C. Never
Explanation
An isosceles triangle is a type of triangle that has two sides of equal length, while an equilateral triangle has all three sides of equal length. Since the definition of an isosceles triangle does not include all three sides being equal, it can never be the same as an equilateral triangle, which requires all three sides to be equal. Therefore, the correct answer is "never".

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• 10.

### A triangle's angles ____________ add to 180*

• A.

Sometimes

• B.

Always

• C.

Never

B. Always
Explanation
The sum of the angles in a triangle is always 180 degrees. This is a fundamental property of triangles and can be proven using various geometric principles. Regardless of the size or shape of the triangle, the sum of its angles will always be 180 degrees.

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• 11.

### A triangle with two 45* angles

• A.

Right

• B.

Acute

• C.

Obtuse

B. Acute
Explanation
A triangle with two 45° angles is an acute triangle. In an acute triangle, all three angles are less than 90°. Since two angles are already 45°, it means that the third angle must also be less than 90° in order for the sum of all angles to be less than 180°. Thus, the triangle is acute.

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• 12.

### A triangle with a 102* angle

• A.

Acute

• B.

Obtuse

• C.

Right

B. Obtuse
Explanation
An obtuse triangle is a triangle that has one angle greater than 90 degrees. In this case, the given triangle has an angle of 102 degrees, which is greater than 90 degrees, making it an obtuse triangle.

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• 13.

### A triangle in which all angles measure 60*

• A.

Obtuse

• B.

Scalene

• C.

Aute

C. Aute
Explanation
The correct answer is "aute." A triangle in which all angles measure 60 degrees is known as an equilateral triangle. In an equilateral triangle, all sides are equal in length, and all angles are equal. Therefore, it cannot be obtuse or scalene.

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• 14.

### A triangle in which side measures are 2m, 4m, and 7m.

• A.

Equianglar

• B.

Obtuse

• C.

Scalene

C. Scalene
Explanation
The given triangle has side measures of 2m, 4m, and 7m. A scalene triangle is a triangle in which all three sides have different lengths. In this case, since all three sides have different measures, the triangle is scalene.

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• 15.

### A triangle in which angle measures are 45*, 55*, and 80*

• A.

Right

• B.

Scalene

• C.

Obtuse

B. Scalene
Explanation
The given triangle has angle measures of 45°, 55°, and 80°. A scalene triangle is a triangle in which all three sides have different lengths. Since the given triangle does not have any equal sides, it can be classified as a scalene triangle.

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• Current Version
• Mar 21, 2023
Quiz Edited by
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• Oct 17, 2009
Quiz Created by
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