What Kind of Triangle is ABC in a Square with an Isosceles Triangle?

In summary, the conversation discusses how to determine the type of triangle ABC, which is inside a square ABDE. By creating an isosceles triangle CDE within the square and using a hint to create a point F, the answer is revealed to be an equilateral triangle. The use of Euclidean theorems and the suggestion to use the law of cosines are also mentioned.
  • #1
chaotixmonjuish
287
0
I have this question:

Inside a square ABDE, take a point C so that CDE is an isosceles triangle with angles 15 degrees at D and E. What kind of triangle is ABC?

I put C close to the bottom to get my isosceles triangle. According to the answer in back, the triangle ABC is equilateral. The hint that went along with the answer is pick a point F to make a triangle congruent to triangle CDE. Are there theorems that I am missing to see how this could work out? I've spent a while on this and I feel like I'm missing something obvious.
 
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  • #2
have you tried law of cosines?
 
  • #3
In this excercise, I have to do the proof using various Euclidean theorems. It's a practice excercise from Coxeter's Geometry book. The hint says to create a point F such that BF is perpendicular to CD aof the equilateral triangle CDF. Hence BC=BD=AB: and ABC is equilateral

I'm not sure how that happens
 

1. What is College Euclidean Geometry?

College Euclidean Geometry is a branch of mathematics that deals with the study of shapes, sizes, and properties of figures and objects in a two-dimensional plane. It follows the principles and axioms laid out by the ancient Greek mathematician Euclid in his book "Elements".

2. What are the main topics covered in College Euclidean Geometry?

The main topics covered in College Euclidean Geometry include points, lines, angles, triangles, circles, polygons, and transformations. It also covers concepts such as congruence, similarity, and symmetry.

3. How is College Euclidean Geometry different from High School Geometry?

College Euclidean Geometry is more advanced and rigorous compared to High School Geometry. It delves deeper into the theoretical foundations and proofs of geometric concepts, rather than just focusing on solving problems. It also covers topics that are not typically taught in high school, such as non-Euclidean geometries.

4. What are some practical applications of College Euclidean Geometry?

College Euclidean Geometry has many practical applications in fields such as architecture, engineering, computer graphics, and physics. It is used to design and analyze structures, create visual representations of objects, and model real-world situations.

5. What skills are needed to succeed in College Euclidean Geometry?

To succeed in College Euclidean Geometry, one needs to have a strong foundation in algebra and a good understanding of basic geometric concepts. It also requires critical thinking, logical reasoning, and the ability to construct and write proofs. Good visualization skills and attention to detail are also important.

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