Download 7.4 Special Right Triangles Activity Special Right

Special Right Triangles activity (worth 30 points if completed, this must be turned in on 3/13/14)
Group members:___________________________________________________
To begin: What is the Pythagorean Theorem?
Draw an isosceles right triangle. Find the measures of all the angles of the triangle.
Does every isosceles right triangle have the same angle measures? Why or why not?
Draw another isosceles right triangle. Is this triangle similar to the first one you drew? If it is, name the
theorem that shows the triangles similar, if it is not, explain why.
Pick a leg length for the first triangle you drew. Find the measures of all the other sides, don’t use
decimals.
Pick a different leg length for the second triangle you used. Find the measures of all the other sides,
don’t use decimals, keep the answer in radicals.
To this point you have earned 8 points. You will 5 more points for finding the missing sides correctly
5√2
6√2
Type equation here.
2 points- if you know the legs of an isosceles right triangle, how can you find the hypotenuse without
using the Pythagorean Theorem ? Either use pictures or words to explain
10
30-60-90 Triangles
Draw an equilateral triangle. Pick a length for all three sides and find the angle measure for all three
angles.
Draw a perpendicular bisector inside your equilateral triangle. Redraw just one of the right triangles
you created so it is by itself. Label all the angle measures and find the measures of all the sides. (Be
careful to identify a, b, and c for the Pythagorean theorem).
Draw another right triangle with angle measures of 30, 60 and 90. Given the shortest side has a length
of 5, find the length of the other side and the hypotenuse. Use the equilateral triangle and your right
triangle from the problem before as a guide.
To this point you have earned 23 points if all other questions are completed. Find the missing lengths to
12
the sides for another 5 points.
30°
60°
15
18
10√3
30°
60°
2 points: What’s the relationship between the angles and the sides of a 30-60-90 triangle?
A
B
45°
C
90°
60°
60°
90°
a
5
b
30°
c
3√3
19/3
2√3
45°
5√2
2
30
7√3
3
45
7√3
3
45°
10
For 5 bonus points,
fill in the chart
correctly with all
values. No
decimals.