Can triangles with the same side lengths have different angles?

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In summary, there is no other triangle with the same side lengths as ABC (4, 4, and 7) but with different angles, as this would violate the SSS and CPCTC congruency criteria. Drawing a visual representation may not always help in determining the validity of such questions.
  • #1
akarikairi
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△ABC has side lengths 4, 4, and 7.
Is there another triangle with the same side lengths but different angles?

I get a lot of questions like these, and I don't know how to judge whether or not they are true or false. Drawing them on paper doesn't always help me either, but I do try to - to get a visual representation of the questions.
 
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  • #2
Hi akarikairi,

If there was another triangle with the same side lengths, then by SSS the two triangles would be congruent. Then by CPCTC the corresponding angles are congruent. So there is no triangle with the same side lengths as ABC but with different angles.
 
  • #3
Thank you for the explanation! This is very helpful.
 

Related to Can triangles with the same side lengths have different angles?

What is the difference between sides and angles?

Sides refer to the length of a line segment that connects two points on a shape, while angles refer to the measurement of the opening between two intersecting lines or line segments.

How are sides and angles related?

Sides and angles are related through the properties of a shape. The number of sides determines the number of angles, and the angles determine the shape's characteristics, such as its symmetry and whether it is regular or irregular.

Can a shape have more sides than angles?

No, a shape cannot have more sides than angles. This is because each angle is formed by two sides, so the number of angles will always be equal to or greater than the number of sides.

Which is more important, sides or angles?

Both sides and angles are equally important in determining the properties and characteristics of a shape. Without either one, a shape would not exist or have a defined form.

How do sides and angles affect the perimeter and area of a shape?

The length of the sides affects the perimeter of a shape, while the angles determine the area. In general, the more sides a shape has, the larger its perimeter will be, and the larger the angles, the greater the area will be.

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