Thank you for sharing the image. I see the task is to solve for the missing measures in quadrilaterals that are rhombuses. Let me extract the necessary information and calculate the missing values. PIL import Image import pytesseract

Load the image from the uploaded file

image_path = '/mnt/data/17386956007316wiikg88.jpg' image = Image.open(image_path)

Use OCR to extract text

extracted_text = pytesseract.image_to_string(image)

Display the extracted text for analysis

extracted_textThe text extracted from the image is incomplete and not entirely clear. However, I understand that the task involves solving for missing measures in rhombuses with given properties. I will use the visible data from the image to analyze each case:

1. Rhombus properties: All sides are equal, and diagonals bisect each other at 90°.

Solving the problems:

1. JK = 12 and JN = 7

• Find JM, JL, MN, MK:
  • All sides of a rhombus are equal: $JK = JM = JL = MK = 12$.
  • Diagonal JN is bisected by the other diagonal, so $MN = NK = \frac{JN}{2} = \frac{7}{2} = 3.5$.

2. EF = 23 and DF = 40

• Find GF, HF, GH, GE:
  • All sides of the rhombus are equal: $EF = GF = HF = GE = 23$.
  • Diagonal DF is bisected, so $DH = HF = \frac{DF}{2} = \frac{40}{2} = 20$.

3. RT = 22 and US = 18

• Find VT, UV, RS, ST:
  • All sides of the rhombus are equal: $RT = VT = UV = ST = 22$.
  • Diagonal US is bisected, so $RS = ST = \frac{US}{2} = \frac{18}{2} = 9$.

4. Missing angles in the rhombus

• Based on the diagram, angles in a rhombus:
  • Opposite angles are equal.
  • Adjacent angles sum to 180°.
  • Measurements can be directly deduced.

Would you like me to provide detailed reasoning for any specific part or verify the missing measures further? Let me know! Below are related questions for deeper exploration.

5 Related Questions:

1. How can you calculate the length of a diagonal in a rhombus given the side length and one angle?
2. What properties of rhombuses differentiate them from general parallelograms?
3. How do the diagonals of a rhombus relate to each other geometrically?
4. How can trigonometry be applied to find angles in a rhombus with given side lengths and diagonal lengths?
5. What is the relationship between the diagonals of a rhombus and its area?

Tip:

Always use the property that diagonals in a rhombus are perpendicular and bisect each other for solving geometric problems efficiently.