MHB Solve Proving 2 Triangles Cong. w/ Diam & Eq. Triangle (2-Col Proof)

Click For Summary
To solve the problem of proving two triangles congruent with a diameter and an equilateral triangle, it's essential to start by identifying the given elements. The discussion highlights that if two arcs are congruent, the angles subtending those arcs must also be equal. Additionally, if all three arcs are of equal length, it indicates that the triangle formed is equilateral. The presence of a bisector is suggested as a key component in establishing congruence. Understanding these relationships is crucial for completing the proof.
srk
Messages
1
Reaction score
0
View attachment 5015

Not sure how to solve considering nothing is given as perpendicular or bisected.
Is anyone aware on how to solve this problem?

~S.R.K.
 

Attachments

  • 11.jpg
    11.jpg
    61.5 KB · Views: 119
Mathematics news on Phys.org
Well, to start with list what is given, then look at similar components
 
I think you will see that KH is a bisector and that will all angles equal and the sides equal
 
Last edited:
If two arcs are congruent, what must be true about the angles that subtend the arcs?
 
srk said:
Not sure how to solve considering nothing is given as perpendicular or bisected.
Is anyone aware on how to solve this problem?

If all three arcs have the same length, then the triangle is equilateral.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB Triangle two column proof question
  • · Replies 1 ·
Replies
1
Views
6K
MHB Perpendicular vectors, triangle, tetrahedron
  • · Replies 3 ·
Replies
3
Views
7K
Proving the 2:1 Ratio of a Triangle's Medians at the Centroid Using Vectors
  • · Replies 1 ·
Replies
1
Views
19K
All Triangles are Isosceles Proof (Euclidean Geometry)
  • · Replies 18 ·
Replies
18
Views
5K
Proving # Equilateral Triangles on Sphere
  • · Replies 2 ·
Replies
2
Views
2K
High School How Can You Prove BC^2 Equals BK Times BQ in Equilateral Triangles?
  • · Replies 2 ·
Replies
2
Views
2K
Solving for x in 0 = -1/8 + 3/8 x / (10^2 +x^2)^0.5
  • · Replies 10 ·
Replies
10
Views
3K
Angles inscribed in circles part 1
  • · Replies 6 ·
Replies
6
Views
2K
High School Can You Prove $AB+BC \ge AD+DC$ in a Triangle?
  • · Replies 1 ·
Replies
1
Views
1K
Triangle Problem: Prove (a+1)(b+1)(c+1) < 4
  • · Replies 2 ·
Replies
2
Views
2K