Unit 7 - Similarity Flashcards
What proves 2 figures are similar? (2)
- If there exists a similarity transformation
- Taking 1 figure onto the other figure.
What’s a similarity transformation? (3)
- A composition
- of a finite number
- of dilations/basic rigid motions
What do all similar figures must have?
- Congruent angles
- PROPORTIONAL Sides
(Congruent figures must have congruent sides, but similar only needs proportional)
All CONGRUENT Figures are SIMILAR
But not all SIMILAR figures are CONGRUENT
What are three properties of Similarity Transformations? (3)
- Reflexive (A = A)
- Symmetric (A is sim. B, B is sim. to A)
- Transitive (If A - B, B - C, C - A)
What happens to the figures if they share the same transformations but not a dilation? (2)
- FIgures are congruent
- Figures are similar
What is the Angle - Angle Similarity Theorem? (3)
- If two angles of one triangle
- Congruent to two angles of other triangle
- Triangles are similar
How do you prove a proportion?
Corresponding sides of similar triangles are in proportion.
How do you prove that two triangle are similar?
AA Sim. Thm.
How do you prove that the cross multiplication is valid in similar triangles?
The product of the means = The product of the extremes
What is the SAS Similarity Theorem? (3)
A triangle can be proven similar through SAS if…..
1. One pair of congruent angles
2. Sides adjacent to angles are in proportion
3. If the SF between pair of corr. sides are congruent to the SF of the other pair of corr. sides, the sides are in proportion
What is the SSS Similarity Theorem? (2)
A triangle can be proven similar through SSS if…..
1. All sides are in proportion
2. If SF between a pair of corr. sides are equal to the SF of the other pair of corr. sides, the sides are in proportion
What is the Perimeter of Similar Polygons?
Side/Side = Perimiter/Perimeter
What is the Area of Similar Polygons?
(Side)² / (Side)² = Perimeter/Perimeter
