How Do Triangle Similarity and Supplementary Angles Relate in Geometry?

  • Thread starter Thread starter kiyoshi7
  • Start date Start date
  • Tags Tags
    Area Homework
AI Thread Summary
Triangle similarity is closely related to supplementary angles in geometry, particularly in high school curricula. The discussion highlights that the triangle problem involving a single square demonstrates how supplementary angles at the vertices of the triangle lead to the conclusion that the smaller triangles formed are similar. This similarity allows for the establishment of equal ratios of corresponding sides among the triangles. Additionally, all three smaller triangles in the problem are identified as right triangles, which further supports the application of triangle similarity principles. Understanding these concepts is essential for solving related geometric problems effectively.
kiyoshi7
Messages
7
Reaction score
0
Moved to homework area sorry.
-kiyoshi7
 

Attachments

  • 001.jpg
    001.jpg
    15.2 KB · Views: 417
  • 002.jpg
    002.jpg
    14.8 KB · Views: 432
Last edited:
Mathematics news on Phys.org
kiyoshi7 said:
I'm not looking for an answer to these questions but orientation on what to study.

similarity :wink:
 
Last edited:
Study Triangle Similarity and study Supplementary Angles, from the standard high school Geometry course. The triangle problem with the single square relies on supplementary angles where the upper right and left square vertices meet two sides of the larger triangle. You can conclude that all three of the smaller triangles are similar, and so the ratios of their corresponding sides are equal. A proportion can be arranged for the two smaller left & right-hand triangles; and note too that all three of the smaller triangles are RIGHT triangles.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

I Help with area formula using direction cosines
Replies
3
Views
2K
MHB What is the Minimal Area of a Right-Angled Triangle with an Inradius of 1 Unit?
Replies
1
Views
1K
MHB [ASK] Find the ratio of the area of triangle BCH and triangle EHD
Replies
4
Views
2K
MHB How can I find the area of a triangle with a given angle and two sides?
Replies
2
Views
1K
MHB Area of Triangle ABC: Find the Answer Here
Replies
2
Views
1K
I Chiral symmetries in E[SUP]^n[/SUP]
Replies
1
Views
2K
MHB Find the areas of segment in circle
Replies
1
Views
2K
MHB Why Can't a Right Triangle Have Sides that Add Up to the Area of Squares?
Replies
2
Views
2K
MHB What is the smallest side length BC of triangle ABC with fixed angle and area?
Replies
2
Views
1K
MHB How Do I Find the Area of a Triangle with Non-Intersecting Vertices?
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top