Geometry
Ch. 7 Right Triangles and Trig
7.5: Investigating Right Triangle Ratios
Name: ________________________________
Date: _________________________________
Essential Question: How can you find a leg of a right triangle when you know the other leg and one acute
angle?
Step 1: In the figure to the right you will find a 40 degree angle. A point has been marked every 2
centimeters on a side as shown. Perpendicular segments have been drawn through the 3 points.
Step2: Measure the legs of each right triangle. Copy and complete the table.
Triangle
Adjacent
Leg
ΔABC
2 cm
ΔADE
4 cm
ΔAFG
6 cm
𝑶𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝑳𝒆𝒈
𝑨𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝑳𝒆𝒈
Opposite
Leg
𝐵𝐶
𝐴𝐶
𝐵𝐶
Step 3: Explain why the proportions 𝐷𝐸 = 𝐴𝐸 and 𝐴𝐶 =
𝐷𝐸
𝐴𝐸
are true.
Step 4: Make a conjecture about the ratio of the lengths of the legs in a right triangle. Test your conjecture
by making your own diagram. Draw a different size angle and 3 points on one of the sides 3 cm apart.
(Show your test!)