Move slider $latex \alpha$ to the extreme right.
1.) What do you observe? What is the area of the larger square (green and red regions)?
2.) Move slider p to the extreme right. What is the area of the figure formed in terms of a and b?
3.) What can you say about the area of the square in Question 1 and the area of the figure in Question 2?
4.) What equation can you form using the areas of these squares?
To construct a triangle congruent to triangle ABC, move the slider to the right. To see the construction steps, move the slider slowly to the extreme right.
The applet above shows that if the three corresponding sides of two triangles are congruent, then the two triangles are congruent.
Given below is a parallelogram with base b and height h. Move points A and B determine the shape and size of the parallelogram, and then move the red point to the extreme right and observe what happens.
- If the red point is on the extreme right of the segment, what shape is formed? Justify your answer.
- What is the area of the shape in Question 1?
- How is the area of the shape in Question 1 related to the area of the original figure?
- What is the area of the parallelogram in terms of b and h?
- What can you conclude about the area of the parallelogram in the original figure and the area of the shape in Question1?
Given below is a trapezoid with bases b1 and b2 and height h. Move the slider to the extreme right and observe what happens.
- When alpha is 180 degrees, what shape is formed? Justify your answer.
- How is the area of the shape in 1 computed based on the figure?
- What is the relationship between the area of the shape in 1 and the area of the trapezoid?
- What formula will describe the area of the trapezoid based on the given above?