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.

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Presentation 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.

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