Introduction
Similar Figures are one topic we learmed about this year. It is used to find solutions of one shape or object by using the measures already found on another corresponding shape or object.
Task
I will be showing you the steps to solve Similar figures, Prove similar Figures congruent, and Real worl examples of when you would use the Similarity properties.
Process
Shapes are similar if they are the same shape, but not the same size.
Rotation is one example. These are both Triangles, both have congruent sides, but one triangle is rotated. They are similar because they are the same shape with the same measures. But one is rotated.
Reflection is another example of Similarities. If you look at the measures of the larger triangle, and the measures of the smaller triangle, you will see that the measures of the smaller triangle are half the size of the larger triangle. The smaller figure and the larger figure are both triangles, since one is smaller, they are similar.
SSS- SSS Similarity(Side Side Side Similarity) is when there are 3 sides that are corresponding, no angles are corresponding.
ASA-ASA Similarity (Angle Side Angle Similarity) is used when there are two congruent angles, and one congruent side in between the two angles.
SAS- SAS Similarity (Side Angle Side Similarity) is used in a situation where there are two congruent sides of a triangle, with one congruent angle in between the corresponding angles.
AAS- AAS Similarity (Angle Angle Side Similarity) is used in an instance when there are two congruent angles and one congruent side, in that exact order.
HL- HL Similarity (Hypotenuse Leg Similarity). This Theorem states that any two right triangles that have a congruent hypotenuse and corresponding congruent legs are similar/congruent.
CPCTC- Corresponding Parts of Congruent Triangles are Congruent.
Proving Similarities
HJ is perpindicular to KI- Given
Definition of Perpindicular Lines- <HJK and <HJI
∆HJK and ∆HJI are right triangles- A right triangle has a right angle
HJ is congruent to HJ- Reflexive property of congruence
HI is congruent to HK- Given
∆HJK is congruent to ∆HJI- hypotenuse leg postulate
KJ = JI- CPCTC
Evaluation
Corresponding sides and angles
Conclusion
Similarity is a good subject to know, it will always benifit to have knowledge of the subject.
Credits
Most people might think that the subject Similarity is boring but i think it is interesting, and that most people should learn ot, it can make problems a lot easier. For example, Take the measurements of a building and you will be able to find the measures of a similar building by using the theorems of Similarity.
Practice similarities on IXL, and get gold on all of them.
http://www.ixl.com/math/geometry/identify-similar-figures
http://www.ixl.com/math/geometry/similarity-ratios
http://www.ixl.com/math/geometry/side-lengths-and-angle-measures-in-sim…
http://www.ixl.com/math/geometry/similar-triangles-and-similarity-trans…