Date _________________ Item _______
30-60-90 Triangle Discovery
1. Observe
ΔPQR
. Use patty paper to trace one of the angles, and then compare it to the
other angles. Confirm that the triangle is equiangular.
Use what you know about the sum of the angles in a triangle to determine the angle
measures.
∠P=____
∠Q=____
!!!!!!!!
∠R=____
Record the measures for
∠P
and
∠R
on the diagram. Do not record the measure for
∠Q
on the diagram.
2. Use a straightedge to draw an altitude starting at point Q. This altitude should intersect
PR
where you see a point. Label this point S.
Use what you know about altitudes and the sum of the angles in a triangle to determine the
angle measures.
∠QSR =____
∠SQR =____
Record the measures for
∠QSR
and
∠SQR
on the diagram.
3. Use patty paper to trace
ΔQRS
and compare it to
ΔQPS
. What do you notice?
4. Focus on the full triangle again--
ΔPQR
. Use patty paper to trace one of the sides, and then
compare it to lengths of the other sides. Confirm that the triangle is equilateral.
The triangle is shown on centimeter paper. Record the lengths of the following segments.
RS =____
QR =____
How did you determine the measure of
QR
?
