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In the figure, $D$ is the midpoint of $\overline{A C}$.a. Find $A C, D C,$ and $D B$b. Use your results from part a to help you explain why $\triangle A B C \sim \triangle C D B$

a. $$\begin{array}{l}A C=\sqrt{2} \\D C=\frac{\sqrt{2}}{2} \\D B=\frac{\sqrt{2}}{2}\end{array}$$b.

Geometry

Chapter 7

Similarity

Section 2

Ratios in Similar Polygons

Polygons

Johns Hopkins University

Piedmont College

Utica College

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and this problem. We have a triangle that looks like this ABC with point d here. And we're also given some values that this is a right angle. This is the right angle. This is one and this is one. So for a we want to find the values of a, C, D. C and D. B. So it tells him the problem that Di is in the point of a sea. So we know that these to values, whatever they are, they're gonna be equal to each other. So we can use this big triangle here, since it's a right triangle, we can use for that grand theorem to figure out the length of this side here. So let's do that. So we have a squared, which is one squared B squared, which is one squared equals C squared. So one player, one square plus one squared is too. And then we can square root both sides. So see is going to equal the skirt of two. So this whole side is going to equal the spirit of two. So that is our A C. So we know that a D and D C are congruent, so they're going to be half of spirit of two. So this one is gonna be squirted two divided by two. And this one is gonna be escorted to divided by two. So D c is gonna be scored a two divided by two to find the last measure. So since I know that the sides of this big Triangle ABC are the same, that means these angles have to be the same. So this is 45 and this is 45 which makes this angle 45 as well and this 1 45 as well. So it means that the size of this triangle have to be the same. So d b would also be squared to over two. Now for part B, it says from results from part, eh, explain why that Triangle ABC. It's similar to triangle C D B well again, we can look at the angle measures and see that the angles are all the same. So, on this one on the big triangle we have a 90 of 45 45 and then in the small triangle. We also have a 90 of 45 in a 45. So by angle angle, the two triangles are congruent, so because all three angles are congruent, the triangles are similar

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