Study Guide And Intervention Similar Polygons
Similarity statement if the figures are similar. Each pair of polygons is similar. Write a similarity. Study Guide and Intervention.
Unit 6 study guide by Isaac Grunberg Are these similar? Find scale factor The ratio of the lengths of two corresponding sides is a scale factor.
Find the value of x Pratice problems Answer key 1. The triangles are similar 2. X=2 6.1 Use similar polygons Two polygons are similar if the corresponding angles are congruent and the corresponding side lengths are proportional. These triangles are similar because they have congruent angles and have corresponding side lengths.
20/10=12/6=17/7 The scale factor is 2:1 because 20/10=2/1, 12/6=2/1,14/7=2/1 You write a proportion: DE/AB=DF/AC Then substitiute: 10/5=15/x cross product: 5x15=75/10=7.5 x=7.5 1. Are these triangles similar? Write the scale factor for the triangles. 6.2 Relate transformations and similarity Dilation: A dilation is a transformation that preserves angles measures and results in an image with proportional lenghts to the original figure. Dilations and Similartiy If a dilation can be used to move one figure onto another, the two figures are similar. Describe the transformation Describe the transformation that moves the red triangle onto the blue. Dilation Practice problems 1.
What type of transformation is ABC to AED? Are triangle ABC and triangle AED proportional? Answer key 1.
Yes they are proportional. 6.3 Prove triangles similar by AA Angle-Angle similarity: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Prove triangles are similar Show the two triangles are similar. Your know angles TUW and XUV are congruent becuase of the vertical angles congruence theorem. TW and VX are parallel so angle s is congruent to angle u by alternate interior angles therorem so TUX is similar to VUX. Use AA 26 64 Are the triangles similar? H K G D E C D and G are congruent because they are both right angles.
Study Guide And Intervention Similar Polygons
Beucase of the triangle sum theorem, 26+90=+angle E=180; so angle E=64. Therefore angle E and angle H are congruent. The triangles are similar. Practice problems 48 42 1.
Are these two triangles similar? Write a similarity statement. Answer key 1. They are similar. F G H K L J 2.
FGH is similar to KLJ. Prove triangles similar by SSS and SAS SSS similarity theorem: If the corresponding sides lengths of two triangles are proportional, then the triangles are similar. Find the similar triangles 8 12 16 12 10 8 12 9 6 To find the similar triangles you have to group the shortest sides and the longest sides. Shortest: 8/6=4/3 Longest: 16/12=4/3 Remaining: 12/19=4/3 The ratios are equal so triangle 1 is congruent to triangle 2.
Use SSS 4 x-1 8 3(x+1) 18 4 4/12=x-1/18 4 x 18= 12(x-1) 72=12x-12 x=7 SAS: If any two sides of a triangle are equal in length to two sides of another triangle and the angles between each pair of sides have the same measure, then the two triangles are congruent; that is, they have exactly the same shape and size. Problem questions 1. Are any of the triangles similar to each other? Write a similarity statement.
12 7 8 6 7 11 3.5 4 6 A B C J K L R S T Answer key 1. ABC and RST are similar 2. AVC is similar to RST 6.5 Use proportionality theorems Triangle proportionality theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. Converse: If a line divides two sides of a triangle proprotionally, then it is parallel to the third side. Find length of a segment 4 6 9 DB/DA=BE/CE DB/9=4/6 9x4=36/6=6 Theorem 6.6: If three parallel lines intersect two transversals, then they divide the transversals proportionally. Theorem 6.7: If a ray bisects an angle of a triangle, then it divides the oppote side into segments whose lengths are proportional to the lengths of the other two sides.
Practice problem 90 50 40 x 1. Find the value of x 2.
Write a similarity statment Answer key 1. X=72, 40/50=90/x 2. Triangle BDE is similar to triangle BAC 6.6 Perform similarity transformations Dilation or reduction? What transformation is the green to the red?
Dilation Dilation or reduction? What transformaion is the red to blue?
Reduction Practice problems What kind of transformation is the blue to the red? Answer key 1. Dilation Conclusion In conclusion, this study guide helped me study for the test as well as it could help another student. This could be especially helpful for a student who is struggling with the concepts. This is because this is a more concise way of learning the material you need to do well on a test then the book is.
This was helpful for me making it and can be a help to other students.