Construct vertex D of an acute angled triangle

  • Context: MHB 
  • Thread starter Thread starter mathlearn
  • Start date Start date
  • Tags Tags
    Triangle Vertex
Click For Summary

Discussion Overview

The discussion revolves around the construction of vertex D in an acute-angled triangle, focusing on geometric principles and relationships between triangle elements. Participants explore methods for locating point D based on given conditions.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant inquires about initial ideas for constructing point D.
  • Another suggests using the area formula for triangles and encourages a description of the location of D.
  • A participant proposes that both triangles should share the same base and lie between the same pair of parallel lines, hinting at a connection to parallelograms.
  • Another participant clarifies that the problem requires CA to equal CD, recommending the drawing of a line through C parallel to AB to locate D.
  • It is noted that since the triangles share a base, their heights must be the same, which supports the construction method involving a parallel line through C.
  • A method involving the use of compasses to find point D is described, where D is determined by the intersection of a drawn arc and the parallel line.
  • One participant seeks confirmation on the correctness of their understanding.
  • Another participant affirms that the previous explanation is correct.

Areas of Agreement / Disagreement

Participants generally agree on the method for constructing point D, with some clarification and elaboration on the geometric principles involved. However, the discussion includes varying levels of certainty regarding the initial ideas and the specifics of the construction process.

Contextual Notes

Some assumptions about the properties of triangles and the relationships between points may not be fully articulated, and the discussion does not resolve all potential ambiguities in the construction process.

mathlearn
Messages
331
Reaction score
0
a0e4xd.jpg


For a closer look click here

Any Ideas on how to begin?

Many Thanks :)
 
Mathematics news on Phys.org
You know the formula for the area of a triangle. Why don't you describe your ideas on the location of $D$?
 
:) Both the triangles should be on the same base and between same pair of parallel lines

I am not sure whether it correct but here are my ideas

egwh05.jpg


I think It has got to do something with parallelograms, I guess?

Many Thanks :)
 
mathlearn said:
Both the triangles should be on the same base and between same pair of parallel lines
Yes, but the problem statement also stipulates that $CA=CD$. So you should draw the line through $C$ that is parallel to $AB$ and then mark $D$ on that line so that $CA=CD$. To draw a parallel line through $C$, see here.
 
It has to do with the fact that the area of a triangle is "(1/2) base times height". Since the two triangles will have the same base, their heights must also be the same. That is the reason for drawing the line, through C, parallel to AB. The further condition is that "CA= CD". Set one leg of a pair of compasses at C, set the other on A, and draw an arc with center at C and radius CA. D is where the line and arc intersect.
 
Correct ?

vdjvyo.jpg
 
Yes, it's correct.
 

Similar threads

MHB Proving $\angle ABC$ is Acute: Inside the Triangle $ABC$
  • · Replies 4 ·
Replies
4
Views
1K
MHB Proving Equality of Angles in an Acute Triangle
  • · Replies 4 ·
Replies
4
Views
1K
MHB Acute angle of right triangles
  • · Replies 4 ·
Replies
4
Views
2K
MHB Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°
  • · Replies 2 ·
Replies
2
Views
1K
High School Why does the trigonometry of obtuse angles use ref angles?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Finding the dependence of maximum vertex degree on k-colorability
  • · Replies 1 ·
Replies
1
Views
2K
MHB Difference of angles in a triangle
  • · Replies 4 ·
Replies
4
Views
2K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
  • · Replies 1 ·
Replies
1
Views
1K
High School Proof that exterior angles of a triangle sum to 360
  • · Replies 1 ·
Replies
1
Views
2K
High School Understanding the Pythagorean Theorem
  • · Replies 38 ·
2
Replies
38
Views
5K