Can triangles with the same side lengths have different angles?

  • MHB
  • Thread starter akarikairi
  • Start date
  • Tags
    Angles
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
6
0
△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.
 
Mathematics news on Phys.org
  • #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.
 

FAQ: 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.

Similar threads

MHB Difference of angles in a triangle
Replies
4
Views
1K
MHB Minimum Length of Longest Side in Inscribed Triangle
Replies
1
Views
1K
MHB Find Length of Side in Right Triangle w/ 45°, 90°, and 45° Angle
Replies
2
Views
1K
MHB What are the angles of isosceles triangle ABC?
Replies
1
Views
981
MHB What is the smallest side length BC of triangle ABC with fixed angle and area?
Replies
2
Views
1K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
Replies
1
Views
1K
MHB Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°
Replies
2
Views
1K
I Chiral symmetries in E[SUP]^n[/SUP]
Replies
1
Views
1K
MHB Why Can't a Right Triangle Have Sides that Add Up to the Area of Squares?
Replies
2
Views
2K
MHB Calculating Triangle Side Length with Known Angles and Radius
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top