SRT.2 Similarity Notes 2
SRT.2 I can use similarity conditions, congruent angle pairs and proportional sides, to determine if two figures are similar.
Similarity Conditions:[br]1. Congruent Angle Pairs[br]2. Proportional Sides
SRT.2 Conditions of Similarity: 1. Congruent Angle Pairs 2. Proportional Sides
Similarity Conditions: Congruent Angle Pairs
Using Similarity Conditions
Do you think the two triangles are similar? Explain why or why not.
Congruent Angle Pairs & Proportional Sides
If the triangles are similar, use proportional sides to determine the length of side AC
Congruent Angle Pairs & Proportional Sides
If the triangles are similar, use proportional sides to determine the length of side ED
Proportional Sides
Proportional Sides
Write three proportions to represent which sides are proportional to which.[br]Express your three proportions like this: [math]\frac{XY}{ST}=\frac{YZ}{TU}=\frac{ZX}{US}[/math] with the three sides of one triangle in the numerators positions and the proportional three sides of the other triangle in the denominator positions.
the Cross-Produce Rule
Triangles Largest side opposite Largest Angle, Smallest Side opposite Smallest Angle
Similarity Condition: Proportional Sides
If two figures are similar, then every side has a proportional side[br]And if every side of a figure has a proportional side to another figure, then the figures are similar.[br][br]Note: Every side of a figure must be proportional to one side of the similar figure.
Testing triangles for similarity: proportional sides
If any [b]two[/b] triangle are similar, then you should be able to write [b]THREE[/b] proportions, like this [math]\frac{XY}{ST}=\frac{YZ}{TU}=\frac{ZX}{US}[/math][br]Test each pair of triangle, by testing the proportions of each pair. Since you will be testing 3 pairs of triangle, you will need to test 9 proportional statements (three for each pair)[br][br]Which of the triangles above are similar?
For extra help, you may want to work through Khan Academy's Introduction to Similar Triangles
https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-triangle-similarity-intro/v/similar-triangle-basics