Stevens, I Applet
The triangle on the left is a right angle triangle with the altitude YW drawn from the right angle to the hypotenuse.
1. How many triangles do you see on the left side of the screen? Make a conjecture about a relationship between the 3
triangles (XYZ, YWZ, and XWY) as you drag the vertices to change the lengths of the sides and altitude of the triangle.
2. Check to view the measurements of the angles. Use this information to construct a proof for your conjecture.
Note: Feel free to find the measurements of the lengths of the sides to assist you in creating a conjecture or your proof.
3. Knowing this relationship between the triangles, what do we know about the corresponding sides of the triangles? Use this knowledge to write this relationship for the two smaller triangles (YWZ and XWY) and the altitude YW.
Hint: There are two relationships to write.
4. What do you notice about the proportions you wrote in the previous questions and the definition of geometric mean?
5. Let's write two more proportions considering the relationship we found between the triangles. Specifically, consider the ratios that correspond to XZ/YZ.
6. Use the information you learned from your exploration of this triangle to help Zeke and Sky on the right side of the screen. Zeke and Sky are in band together called “The Geometric Meanies”. They want to design a set for their first music video. They need to figure out the height of the wall, but they both left their rulers at home. However, Sky has her lyric book with her and noticed that she could hold the book up to her eyes so that the top and bottom of the book were in line with the top edge and binding of the cover. Based on their heights, they know that Sky is standing 4 feet from the wall and she is holding the book about 2 ft. 8 in. (2.67 ft) .
What is the height of the wall?
Check your answer by clicking on the checkbox in the applet to make
measurement appear on the image.
1. How many triangles do you see on the left side of the screen? Make a conjecture about a relationship between the 3
triangles (XYZ, YWZ, and XWY) as you drag the vertices to change the lengths of the sides and altitude of the triangle.
2. Check to view the measurements of the angles. Use this information to construct a proof for your conjecture.
Note: Feel free to find the measurements of the lengths of the sides to assist you in creating a conjecture or your proof.
3. Knowing this relationship between the triangles, what do we know about the corresponding sides of the triangles? Use this knowledge to write this relationship for the two smaller triangles (YWZ and XWY) and the altitude YW.
Hint: There are two relationships to write.
4. What do you notice about the proportions you wrote in the previous questions and the definition of geometric mean?
5. Let's write two more proportions considering the relationship we found between the triangles. Specifically, consider the ratios that correspond to XZ/YZ.
6. Use the information you learned from your exploration of this triangle to help Zeke and Sky on the right side of the screen. Zeke and Sky are in band together called “The Geometric Meanies”. They want to design a set for their first music video. They need to figure out the height of the wall, but they both left their rulers at home. However, Sky has her lyric book with her and noticed that she could hold the book up to her eyes so that the top and bottom of the book were in line with the top edge and binding of the cover. Based on their heights, they know that Sky is standing 4 feet from the wall and she is holding the book about 2 ft. 8 in. (2.67 ft) .
What is the height of the wall?
Check your answer by clicking on the checkbox in the applet to make
measurement appear on the image.