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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 Do Now Good Things! Unit 4 Review Notes: Congruence vs Similarity ProblemAttic Partner Practice

Good Things!

Unit 4 Review Triangle Congruence Postulates Transversal angle measures Triangle Sum Theorem Exterior Angle Theorem Properties of Isosceles Triangles Triangle Midsegment Theorem

Unit 4 Review Practice Find m<B

Congruence vs Similarity Congruent triangles have congruent angles and congruent side lengths If we perform a rigid transformation on a triangle, we will always have two congruent triangles 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

If we have a point (x,y) and a scale factor of k…. Similar Figures The scale factor is what we multiply each coordinate by Scale factor greater than 1  enlargement Scale factor less than 1  reduction Dilations preserve angle measure If we have a point (x,y) and a scale factor of k…. Dk(x, y) = (kx, ky)

Scale Factor = Scale Factor Length of image side Length of pre-image side = Scale Factor * 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 The scale factor can be written in a variety of ways Decimal Fraction Percentage We always multiply the scale factor – regardless of how it is written! Be careful when using calculator 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 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 would distortions be a bad thing? Why are these bad?

Dilations – Finding the Scale Factor Rectangle ABCD was transformed into rectangle EFGH through a dilation. Enlargement or reduction? Why? How can we determine the scale factor? What is the scale factor of dilation?

Dilations - Vertices 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? I can multiply each coordinate by the scale factor to find the new 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). Is this an enlargement or reduction? What is the scale factor of dilation?

Partner Practice www.problem-attic.com/test/7xda23qf Must show work on a sheet of paper to receive credit for today’s work When you are done, you may begin on this week’s independent practice