Right is Special 2: More Triangles on a Grid
Five 30-60-90 triangles are placed on graph paper. Use the picture below to answer the
following questions:
1. Is there a relationship between the triangles? If so, what relationships exist?
Justify your answer.
2. What relationships occur between two 30-60-90 triangles if each has a short
leg with the same measure?
©2011 Texas Education Agency. All Rights Reserved.
Right is Special 2: More Triangles on a Grid
Answer Key
All five of the 30-60-90 triangles are placed on the graph paper. Using the
graph answer the following questions:
1. Is there a relationship between the triangles? If so, what
relationships exist? Justify your answer.
Any two of the triangles are similar because they are right
triangles and they share an angle at the origin. Corresponding
angles are congruent. Corresponding sides are proportional.
2. What relationships occur between two 30-60-90 triangles if each
has a short leg with the same measure?
The two triangles are congruent because of the Angle Side Angle
Postulate, commonly called ASA.
©2011 Texas Education Agency. All Rights Reserved.
Right is Special 2: More Triangles on a Grid
Scaffolding Notes:
Label the sides of each triangle with
their measurements.
In order to find the length of the
hypotenuse, which formula would be
used?
What is the definition of similar
triangles?
If triangular similarity has been taught,
incorporate the angle, angle, angle
theorem. If not continue below.
Using the information given about the
lengths of the legs of the right triangles,
have students write ratios and compare
the results for each triangle.
The question above provided the
information that all 30‐60‐90 triangles
are similar. What information does the
problem provide about the short side of
both 30‐60‐90 triangles? What is the
ratio of the two short sides? Using the
information above, these are similar
triangles. What can be determined
about the lengths of the long sides?
Use the information you learned from
question number 1 to answer question
number 2.
©2011 Texas Education Agency. All Rights Reserved.