angle – angle similarity, day 2. warm up in an isosceles triangle, the two equal sides are called...
TRANSCRIPT
Angle – Angle Similarity, Day 2
Warm Up
In an isosceles triangle, the two equal sides are called legs and the third side is called the
base. The angle formed by the two congruent sides is called the vertex angle.
The other two angles are called base angles. The base angles of an isosceles triangle are
congruent.
If the vertex angles of two isosceles triangles are congruent, are the triangles necessarily
similar? Explain your thinking.
How can you determine when two triangles are similar?
Two triangles are similar if it can be shown that two angles of one triangle are congruent to two angles of the other triangle.
In nonmathematical situations, similar can be used to mean like or
resembling in a general way. In mathematical terms, similar figures
are similar in a specific way: the corresponding angles are
congruent. The lengths of their corresponding sides are not
necessarily congruent but are proportional.
Are all equilateral triangles similar?
All equilateral triangles have three 60° angles. So, the AA Similarity Postulate holds for all equilateral
triangles.
The AA Similarity Postulate is one way of proving that triangles are similar. The SSS
Similarity Postulate is another way. It states that if the ratios of the measures of the corresponding sides are equal, then
the triangles are similar. The SAS Similarity Postulate is yet another way. It states that if the ratios of the measures of two pairs of
corresponding sides are equal, and the angles formed by those two sides in each triangle are congruent, then the triangles
are similar.
What do you need to show in order to prove that two triangles are similar?
To prove two triangles are similar, you need to prove that at least two angles in one triangle are congruent to two angles in the other triangle. Or, you
can show that the lengths of all three of their corresponding sides are
proportional.
Triangle AGD, shown here, is an isosceles triangle with sides
AG and DG congruent. Two line segments, segments EB
and FC, have been drawn perpendicular to side AD. Use what you have learned about
the AA Similarity Postulate and finding missing measures in similar triangles to describe
how you would find the length of line segment CD.
Exit Ticket