Notes
Name: ___________________________________________
6.7 Similar Right Triangles
Let’s start with an activity!
Below, please trace your right triangle. Be sure to label all sides and angles.
Below, glue the three triangles (“big,” “medium,” and “small”) created when the altitude (height of the triangle) is
drawn from the right angle of a right triangle. Are these triangles similar?! How do you know?
“ Big Triangle”
“Medium Triangle”
“Small Triangle”
If the three triangles above are “similar” to one another, complete the three requested ratios below:
𝐻𝑒𝑖𝑔ℎ𝑡
𝐵𝑎𝑠𝑒
=
=
=
𝐻𝑒𝑖𝑔ℎ𝑡
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=
=
=
𝐵𝑎𝑠𝑒
𝑇𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=
=
=
EXAMPLES: For each of the following right triangles with the altitude drawn, find the value of x, y, and z. You will
want to redraw your three triangles.
1. .
𝑥 = ________________
𝑦 = ________________
𝑧 = ________________
2. .
𝑥 = ________________
𝑦 = ________________
𝑧 = ________________