# Lesson: Similar Triangles

## Comment on Similar Triangles

### Dear Brent.

Dear Brent.
First let me congratulate you for this exceptional site. All the explanations are great. Each video was made in a way that make them understandable and easy to follow. Also the site layout and the graphics of the videos have a pleasing appearance.
I have been studying during the whole summer. I began about May 23 and also I took one math class. I have been doing all of exercises from 2 ETS books. Fortunately I found your site 2 weeks ago. Since then I have being watching all your math videos. Unfortunately I don't have enough time to finished them, my test is on August 1st
I watched all videos lessons from the beginning until the 15th lesson of Geometry. Also I covered all the exercises proposed in each lesson. Are really great. Could you please give an advice to which lessons can be the most important from lesson 15th of Geometry and beyond (numbers lesson from - Integer properties,Statistics, Counting, Probability and Data Interpretation).

Thanks so much, for your help.

### Counting and Probability

Counting and Probability questions are pretty rare on the GRE. If you don't have enough time to complete all of the math lessons, I suggest that you skip those two topics, and complete the other modules (including all of Geometry)

Integer properties, Statistics and Data Interpretation are wayyyyyyyy more important (i.e., tested more often) than Counting and Probability.

### Can you explain the

Can you explain the difference in the Khan Academy method compared to yours. I might just be really tired and not understanding. They put the the ratio as one side of the "smaller" triangle over the other side of the smaller triangle equal to one side of the larger triangle over the other side of the larger similar triangle. Your method puts the side of smaller over the corresponding larger side. Thank you.

### Great question!

Great question!

The methods are interchangeable. Both will yield the correct answer.

Cheers,
Brent

### Hi Brent !!

Hi Brent !!
Is there a way or trick to find which two Corresponding sides / lengths would be the ratio for the two similar triangles

### When comparing any 2 similar

When comparing any 2 similar triangles, the ratio of any pair of corresponding sides is the same.

You want to know how we identify corresponding sides.

Let's say the three angles in BOTH triangles are w, x and y.
So, for EACH triangle, one side will be BETWEEN angles w and x.
Those two sides are corresponding.

Likewise, for EACH triangle, one side will be BETWEEN angles w and z.
Those two sides are corresponding.

And, for EACH triangle, one side will be BETWEEN angles x and z.
Those two sides are corresponding.

Does that help?

Cheers,
Brent

please from this question, https://gre.myprepclub.com/forum/in-the-figure-above-a-is-the-center-of-the-circle-12255.html, how do we know that angle C is 90 degree

Hi Angel,
This is a circle property that says "An inscribed angle that's holding a diameter will always equal 90 degrees.

This property is covered at 2:05 at https://www.greenlighttestprep.com/module/gre-geometry/video/881

Cheers,
Brent

### https://gre.myprepclub.com/forum

https://gre.myprepclub.com/forum/in-the-figure-above-a-is-the-center-of-the-circle-12255.html
Hello,
What do you mean when you say the sides are arranged in triplets ?
Thank you

I didn't use the word triplet in my solution.
However, the person who did use that word is referring to Pythagorean Triplets.
These are commonly-used lengths of right triangles.
The most common example of a Pythagorean Triplet is a 3-4-5 right triangle.
There's also a 5-12-13 right triangle (and others)

For more on Pythagorean Triplet, start watching from 3:25 in the following video: https://www.greenlighttestprep.com/module/gre-geometry/video/867

### https://gre.myprepclub.com/forum

https://gre.myprepclub.com/forum/in-the-figure-above-a-is-the-center-of-the-circle-12255.html
In this question at last will it be 20/40=25/25+y when we are relating the corresponding sides?

In my solution, I'm comparing the corresponding sides of different triangles.
So, for example, the ratio 25/40 is comparing the length of the hypotenuse of one triangle to the length of the hypotenuse of the other triangle.
Likewise, the ratio 20/(25 + y) is comparing the length of one side of a triangle to the length of the corresponding side of the other triangle

With your ratio of 20/40, you are comparing the length of one triangle's LEG with the length of the other triangle's HYPOTENUSE.
This is incorrect.

Does that help?

Cheers,
Brent

### https://gre.myprepclub.com/forum

https://gre.myprepclub.com/forum/topic17317.html

HI Brent,

so in the aforementioned exercise we can just assume that DG=1/2DC?

Yes, you can definitely assume that DG = 0.5(DC)

### Hey, brent, noticed, the

Hey, brent, noticed, the first problem under reinforcements is the quadrilateral. As I have not yet touched on that topic as per your geometry order, I think it would be good to highlight that somehow. After every video, I would like to cement the idea of what I have learned and I don't think it did that for me just now since I have not learned quadrilateral just yet.

Separately, would you suggest that I should complete all the videos first and then come back to reinforcement problems? Because I would like to avoid questions that are yet to be completed from the videos in the order. Please suggest.

### A lot of questions

A lot of questions (especially Geometry questions) test more than one concept.
So, although there's a quadrilateral in the diagram, "similar triangles" is the main concept tested here.
Notice that, from the diagram, we can see that: Area of quadrilateral ABDE = (Area of ∆ABC) - (Area of ∆EDC)
So, to answer the question, we need only find the areas of two triangles.

I suggest you answer reinforcement problems before moving on to the next video. That way, you will get a chance to reinforce what you just learned before moving to the next topic.