Proving ∠D=90°-(∠A/2) in Triangle ABC with Bisectors

In summary, the conversation discusses proving the angle ∠D to be equal to 90°-(∠A/2) when given that ABC is a triangle and the bisector of the exterior angle at B and the bisector of ∠C intersect at point D. The participants also mention potentially drawing the triangle incorrectly or a printing error in the question, but agree that a quick reality check with a simulator or manual construction of the bisectors confirms the given solution. One participant also mentions using a straight-edge and compass to bisect angles, but notes potential difficulties with accuracy.
  • #1
Govind_Balaji
83
0

Homework Statement


ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Then prove that ∠D=90°-(∠A/2)


Homework Equations





The Attempt at a Solution



I guess I want to prove an untrue thing because by drawing a diagram and working out I get ∠D=∠A/2. I think I have drawn it wrong by mis-understanding the question. Or the question is an error? Or did I work out wrong?
 

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  • #2
I get the same result you did and I also oriented the corners of the triangle such that ABC is labelled clockwise instead (C at the top, A at the left), so the intersection point is underneath the triangle and the answer is still the same.
 
  • #3
You can do a quick reality check by drawing an arbitrary triangle and constructing the bisectors and measuring the angles. Try it for several triangles.
 
  • #4
Simon Bridge said:
You can do a quick reality check by drawing an arbitrary triangle and constructing the bisectors and measuring the angles. Try it for several triangles.

It seems a difficult work. Are there any thing to do with Theoretical geometry.
 
  • #5
Even I tried what Simon said with a simulator called GEOGEBRA. I get the same result.
 
  • #6
I get the same result as you using a + b + c = 180° = (180 - b)/2 + b + a + c/2.
 
  • #7
I guess there must be a printing error in the question like may be the angles changed or like that
 
  • #9
Simon Bridge said:
That would be my bet.

Aside: do you not know how to bisect and angle using a straight-edge and a compass?
http://www.mathopenref.com/constbisectangle.html

Yes I know just lazy to do that because when I miss 1° accuracy, I may get very strange results.
 

1. What is an angle in geometry?

In geometry, an angle is a figure formed by two rays that share a common endpoint, also known as the vertex. It is measured in degrees and can range from 0 degrees (no rotation) to 360 degrees (full rotation).

2. How do you classify angles in geometry?

Angles can be classified based on their degree measurements. Acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are between 90 and 180 degrees, and straight angles are exactly 180 degrees. Additionally, angles can be classified as complementary (two angles that add up to 90 degrees) or supplementary (two angles that add up to 180 degrees).

3. How do you solve geometry angle problems?

To solve geometry angle problems, you first need to identify the type of angle and the given information. Then, you can use various formulas and theorems, such as the angle sum theorem or the properties of parallel lines, to find the missing angle measurements. It is important to carefully read and understand the problem before attempting to solve it.

4. What are some real-life applications of geometry angles?

Angles are used in many real-life applications, including architecture, engineering, and navigation. For example, architects use angles to design buildings and structures, engineers use angles to construct roads and bridges, and pilots use angles to navigate airplanes.

5. How can I practice and improve my understanding of geometry angles?

You can practice and improve your understanding of geometry angles by solving various angle problems, using interactive online resources or geometry textbooks, and seeking help from a tutor or teacher if needed. It is important to also understand the underlying concepts and properties of angles to effectively solve problems.

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