This lesson is about similar triangles and similarity theorems. As you go over the exercises you will develop your skills in determining if two triangles are similar and finding the length of a side or measure of an angle of a triangle.
GEOMETRY
Students will be able to understand and apply geometric concepts and relations in a variety of forms.
What are the four similarity theorems?
If in two triangles the corresponding angles are congruent, then the two triangles are similar.
If ΔBOS <> ΔVIC
∠B ≅ ∠V , ∠O ≅ ∠I , ∠S ≅ ∠C
then ΔBOS ~ ΔVIC
If two angles of one triangle are congruent to the corresponding two angles of another triangle, the triangles are similar.
Given: ∠A ≅ ∠O
∠J ≅ ∠B
Then: ΔJAM ~ ΔBON
If in two triangles two pairs of corresponding sides are proportional and the included angles are congruent, then the triangles are similar.
If ΔICE <> ΔBOX

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and ∠C ≅ ∠O
Then ΔICE ~ΔBOX
Examples:
If the two triangles three corresponding sides are proportional, then the triangles are similar.
If ΔSUN <> ΔBLK

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= 

Then ΔSUN ~ ΔBLK
Example:
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2. Explain: Any two congruent triangles are similar.
A. Tell whether the two triangles are similar. Cite the Similarity Postulate or Theorem to justify your answer. (Identical marks indicate ≅ parts.)
B. Determine whether each pair of the following triangles are similar by SAS, AAA, SSS or not at all.
C. Answer the following:
1. Two isosceles triangles have an angle of 50 degrees. Does it follows that the triangles are similar?
2. Two angles of ΔBEL have measures of 20 and 50. Two angles of ΔJAY have measures of 30 and 100. IS ΔBEL ~ ΔJAY ?
3. Is it possible for two triangles to be similar if two angles of one have measures 50 and 75, where as two angles of the other have measures 55 and 70?
4. Two angles of have measures 40 and 80, where as the two angles of the other have measures 60 and 80, are the two triangles similar?
5  6. The lengths of the sides of a triangle are 12 and 15. If the length of the shortest side of a similar triangle is 12, find the lengths of the other two sides.
7 8. In the figure, if AE = 8, AB=4, BC=10, ED=3. Find BD and DC.