On the blank side of the index card, create a design or image to portray a stained glass window. Be creative.

Question

Create your own design with shapes and angles, or draw an image.
Include at least two special angles each of complementary, supplementary, adjacent, and vertical types.
Use a protractor and ruler to ensure straight lines and angle measures when necessary.
Use a pencil to create the design, then use colored pencils or markers for the colors.
Lastly, trace all lines with a black marker using a ruler, to make the lines and angles stand out.
Be sure to indicate the eight angle relationships by labeling or numbering them.
On the back of the index card, create a key that indicates the specified angles and their angle relationship (for example: label two vertical angles as 1 and 2, then indicate on the back vertical angles are 1, 2).
Write four mathematical equations that match the picture for the two complementary and two supplementary angles. Refer to the indication of these angles on the picture as well.

Answer 1

Creating your stained glass window design with the specified angle relationships can be a fun and creative project! Here’s a step-by-step outline of how to create your design and what to include on your index card:

Front Side Design

1. Choose a Theme: Select a theme for your stained glass window. For example, you could choose geometric shapes, flowers, or natural scenery.

2. Draw the Basic Layout: Using a pencil, lightly sketch out your stained glass window. This could be a tall arch shape, emulating traditional stained glass windows.

3. Incorporate Shapes and Angles:

   • Use triangles, rectangles, and circles.
   • Create at least two pairs of complementary angles. For example, one pair can be formed where a triangle meets a rectangle (e.g., angles measuring 30° and 60°).
   • Create two pairs of supplementary angles. For instance, an angle of 120° next to one of 60°.
   • Include adjacent angles, for example, two angles that share a side.
   • Include vertical angles created by two intersecting lines.

4. Number the Angles:

   • Label each angle (1-8) on the design:
     • Complementary angles: Label them as 1 and 2.
     • Supplementary angles: Label them as 3 and 4.
     • Adjacent angles: Label them as 5 and 6.
     • Vertical angles: Label them as 7 and 8.

5. Trace the Design: Use a black marker and a ruler to trace over the pencil lines to enhance visibility.

6. Color the Design: Use colored pencils or markers to fill in each shape with vibrant colors, making it look like a stained glass window.

Back Side Key

1. Create a Key: On the back of the index card, create a key to indicate the angle relationships based on your labels from the front:

   • Angles 1 & 2: Complementary Angles (1 + 2 = 90°)
   • Angles 3 & 4: Supplementary Angles (3 + 4 = 180°)
   • Angles 5 & 6: Adjacent Angles (Share a side)
   • Angles 7 & 8: Vertical Angles (Angle 7 = Angle 8)

2. Mathematical Equations:

   • For complementary angles, let’s say Angle 1 = 30° and Angle 2 = 60°:
     • Equation 1: 30° + 60° = 90°
   • For supplementary angles, let’s say Angle 3 = 120° and Angle 4 = 60°:
     • Equation 2: 120° + 60° = 180°
   • Additionally, you could define angles for the adjacent and vertical angles if desired (e.g., if Angle 5 is 40°, then Angle 6 would be 140°).
     • Equation 3 (Adjacent): 40° + 140° = 180°
   • For vertical angles, such as Angle 7 = 80° and Angle 8 = 80°, use:
     • Equation 4: Angle 7 = Angle 8.

Final Touches

• Review both the front and back of the index card to ensure clarity in your design and keys, making sure all specified angles and relationships are properly identified.

This creative design not only adds aesthetic appeal but also integrates geometrical concepts in a tangible format! Enjoy your artistic and mathematical project!