arc in circle

[shahar]

The question is:


Given: Arc BC size is 70 degree.
Arc AB = Arc AC.
Find the size of the arcs AB and AC.
The source:
נתון: הקשת BC היא בת 70 מעלות.
AB = AC
מצאו את גודל AB ו-AC במעלות.
How to solve it in Geometric Proof solution.
I know to caculate it as (360-70) /2 to each arc.
How I can formulate it as Geometric Proof.

 

[The Highlander]

The question is:
View attachment 39986

Given: Arc BC size is 70 degree.
Arc AB = Arc AC.
Find the size of the arcs AB and AC.
The source:
נתון: הקשת BC היא בת 70 מעלות.
AB = AC
מצאו את גודל AB ו-AC במעלות.
How to solve it in Geometric Proof solution.
I know to caculate it as (360-70) /2 to each arc.
How I can formulate it as Geometric Proof.

I don't understand the Hebraic content of your post but, unless it is saying something you haven't translated, I'm at a loss to know what you mean by a "Geometric Proof".

Given that \(\displaystyle \overset{\frown}{BC}=70°\text{ and }\overset{\frown}{AB}=\overset{\frown}{AC}\) your "calculation" \(\displaystyle \left(\overset{\frown}{AB}=\overset{\frown}{AC}=\frac{360°-70°}{2}=145°\right)\) is absolutely correct.

Why would you need anything more?

 

[fresh_42]

How do you describe [imath] \measuredangle (BMC) = 70° [/imath] geometrically? [imath] \overset{\frown}{AB}=\overset{\frown}{AC}[/imath] is a definition. It establishes a symmetry that you can use. But in order to "compute" something geometrically, you need a geometric input.

 

[The Highlander]

How do you describe [imath] \measuredangle (BMC) = 70° [/imath] geometrically? [imath] \overset{\frown}{AB}=\overset{\frown}{AC}[/imath] is a definition. It establishes a symmetry that you can use. But in order to "compute" something geometrically, you need a geometric input.

I understand that less than the Hebraic.

 

[fresh_42]

I understand that less than the Hebraic.

נניח שהזווית היא 60°. אז אפשר לשאול מדוע אחת הזוויות גדולה פי שניים וחצי מכך. אבל איך אפשר בכלל לתאר גיאומטרית את 145°, הפתרון?
(Google Translate is fun!)

Let's say the angle is 60°. So we could ask why one of the angles is two and a half times larger. But how can we even geometrically describe 145°, the solution?

 

[shahar]

I don't understand the Hebraic content of your post but, unless it is saying something you haven't translated, I'm at a loss to know what you mean by a "Geometric Proof".

Given that \(\displaystyle \overset{\frown}{BC}=70°\text{ and }\overset{\frown}{AB}=\overset{\frown}{AC}\) your "calculation" \(\displaystyle \left(\overset{\frown}{AB}=\overset{\frown}{AC}=\frac{360°-70°}{2}=145°\right)\) is absolutely correct.

Why would you need anything more?

No. I understand the geometric proof changes from place to place. I know in Israel, we can answer the question wiith table of argument and reason (to the argument). Isn't it in English Mathematics? (?!)

 

[The Highlander]

No. I understand the geometric proof changes from place to place. I know in Israel, we can answer the question wiith table of argument and reason (to the argument). Isn't it in English Mathematics? (?!)

This video may help you...

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From "Google" (qv) there is the following advice:-

A geometry proof is a logical, step-by-step argument that establishes the truth of a geometric statement using definitions, postulates, and theorems. It typically starts with given information, moves through logical deductions, and concludes with the assertion to be proven, often organized as a two-column, paragraph, or flow chart proof.

and these guidelines/tips...



Key Elements of Geometry Proofs:

• Diagrams: Always draw and mark the figure with given information, such as congruent sides or angles.
• Given and Goal: Clearly list what is known (hypotheses) and what needs to be proven.
• Logical Steps: Each step must follow from the previous one, with a valid reason (e.g., midpoint definition, Angle Addition Postulate).
• Definitions & Theorems: Reasons are justified by accepted geometric theorems, postulates, and definitions.
• Two-Column Format: The most common structure, featuring numbered statements on the left and corresponding reasons on the right.
  

Common Reasons Used in Proofs:

• Vertical Angles Theorem: Vertically opposite angles are equal.
• Triangle Sum Theorem: Angles in a triangle sum to
  
  .
• Congruent Triangles: SAS, SSS, ASA, AAS, and HL.
• Algebraic Properties: Transitive, substitution, and addition properties.
• Definitions: Midpoint (creates congruent segments), perpendicular (creates angles)
  
  
  
  Tips for Success:
• Do not skip steps: Write down every logical step in the derivation.
• Mark figures: Mark new deductions on your diagram to see the connections.
• Work backward: If stuck, start from the conclusion and figure out what you need to know to reach it.

This other video offers an alternative approach to laying out a proof....

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Hope that helps.

 

[The Highlander]

You may also find (exactly?) what you are looking for here...

Geometric proofs in Hebrew?​

 

[The Highlander]

You may also find these videos on Circle Theorems and their proofs useful in your efforts...
(NB: I suggest you click the (black) "Watch on YouTube" button at the bottom left rather than the (red) "Play" buttons in the middle; the latter plays the video in here while the former opens a new tab where you can watch fullscreen. )

&

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Hope that helps.