424 Do Now 424 What is the solution
- Slides: 17
+ 4/24
+ Do Now 4/24 What is the solution to the equation -5 + √(x-9) = 4? Essential Question: How can we determine the scale factor of dilation?
+ Agenda n Do Now n Good Things! n Unit 4 Review n Notes: Congruence vs Similarity n Problem. Attic Partner Practice
+ Good Things!
+ Unit 4 Review n Triangle Congruence Postulates n Transversal angle measures n Triangle Sum Theorem n Exterior Angle Theorem n Properties of Isosceles Triangles n Triangle Midsegment Theorem
+ Unit 4 Review Practice n Find m<B
+ Congruence vs Similarity n Congruent triangles have congruent angles and congruent side lengths n If we perform a rigid transformation on a triangle, we will always have two congruent triangles n What is the only non-rigid transformation we learned about? Dilations!
+ Congruence vs Similarity Are images that have undergone a dilation congruent to their preimage? ? Unless the scale factor is 1…. NO! They are not congruent, they are similar Similar figures have the same shape, but are different in size
+ Congruent vs Similar
+ Similar Figures n The scale factor is what we multiply each coordinate by n Scale factor greater than 1 enlargement n Scale factor less than 1 reduction n Dilations preserve angle measure If we have a point (x, y) and a scale factor of k…. Dk(x, y) = (kx, ky)
+ Scale Factor Length of image side = Scale Factor Length of pre-image side * You can also use this for coordinate points! What is the scale factor of the dilation (with center at the origin) if point U (5, 7) becomes U’ (25, 35)?
+ Scale Factor n The scale factor can be written in a variety of ways n Decimal n Fraction n Percentage n We always multiply the scale factor – regardless of how it is written! n Be careful when using calculator n Example: We have a triangle ABC. The length of AB is 7 units. After dilating the figure by 75%, what is the length of A’B’?
+ Distortions n Distortions happen when the width and height of a figure are not dilated at the same scale If you can’t find a scale factor that works for the height AND the width, it’s a distortion! Why are these bad?
+ Dilations – Finding the Scale Factor n Rectangle ABCD was transformed into rectangle EFGH through a dilation. n Enlargement n How or reduction? Why? can we determine the scale factor? n What is the scale factor of dilation?
+ Dilations - Vertices n As long as we know the coordinates OR the lengths of the sides, we can find the scale factor A triangle has vertices G(2, – 3), H(– 6, 2), and J(0, 4). If the triangle is dilated by a scale factor of 0. 5 through center C (0, 0), what are the image vertices? A triangle has vertices A(7, 10), B(7, 5), and C(-1, 5). If the triangle is dilated by a scale factor of 2. 5 through the center C(0, 0), what are the image vertices?
+ Dilations – your turn! Triangle MNO has the following vertices: M (-5, 8), N(7, 3), and O(-10, -4). After being dilated, triangle M’N’O’ now has the following vertices: M’(-3. 75, 6), N’ (5. 25, -2. 25), and O’(-7. 5, -3). a. Is this an enlargement or reduction? b. What is the scale factor of dilation?
+ Partner Practice www. problem-attic. com/test/7 xda 23 qf n Must show work on a sheet of paper to receive credit for today’s work n When you are done, you may begin on this week’s independent practice
