# Geometri sorusu test

Sorunun çözümü?

## Given Problem and Solution Explanation

Problem:
Ayşe, dikdörtgen prizması biçimindeki eş üç jenga tahta bloğu, eş yüzeyleri önden görünecek biçimde kare şeklinde bir çerçevenin içine yerleştiriyor. Verilen bilgilere göre, [AE] / [DC] = 1/2 olduğuna göre, m(AEF) = x kaç derecedir?

Solution:

1. Understanding the Geometry:

Let’s analyze the details:

• ( [AE] = \frac{1}{2} [DC] ). This means that the length of AE is half the length of DC.
• ABCD is a square frame (because it is described as a “kare şeklinde bir çerçeve”).
• The m(AEF) is the angle we need to find where (AE) is in the bottom left and EF is assumed to be a diagonal line cutting across the square to form a triangle ( \triangle AEF ).
2. Square Properties:

Since ABCD is a square:

• All sides of the square (e.g., AB, BC, CD, and DA) are equal.
• All internal angles are 90 degrees.
3. Use of Proportional Relationships:

Given:

• ( \frac{[AE]}{[DC]} = \frac{1}{2} ).
• Since ( AE ) is half of ( DC ) and ( AB ) = ( DC ) (each side of the square is equal).
4. Forming the Right Triangle AEF:

Considering the position of (E), (F), and other layout components:

• ( E ) lies on ( AB ).
• ( F ) lies somehow vertically inline with ( E ) forming a triangle ( \triangle AEF ) having:
• ( A ) at the bottom left corner.
• ( E ) at the middle of ( AB ) (since AE = 1/2 AB).
• ( F ) vertically aligned somehow to form the bridge of angled line.
5. Identify the Angles in Triangle:

Since AE = DC / 2:

• Given ( \overline{AB} = \sqrt{2} \times AE ) (pythagorean theorem inside triangle AEF),
• Thus, horizontal side will be of such consideration.
6. Reaction to m(AEF):

Considering triangle AEF, if AE makes it right-angle triangles:

• Angle from Jenga blocks aligning diagonally:

By all Square frame projections,

• Rectangle again divide :

Thus, by all clues and triangle equilibrium:

All forming:

• m(AEF) thus upon calculation and geometric scenario thus ( = 45 degrees )