yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Non-congruent shapes & transformations


2m read
·Nov 10, 2024

  • [Instructor] We are told, Brenda was able to map circle M onto circle N using a translation and a dilation. This is circle M right over here. Here's the center of it. This is circle M, this circle right over here. It looks like at first, she translates it. The center goes from this point to this point here. After the translation, we have the circle right over here. Then she dilates it. The center of dilation looks like it is point N. She dilates it with some type of a scale factor in order to map it exactly onto N. That all seems right.

Brenda concluded, "I was able to map circle M onto circle N using a sequence of rigid transformations, so the figures are congruent." Is she correct? Pause this video and think about that. Let's work on this together. She was able to map circle M onto circle N using a sequence of transformations. She did a translation and then a dilation.

Those are all transformations, but they are not all rigid transformations. I'll put a question mark right over there. A translation is a rigid transformation. Remember, rigid transformations are ones that preserve distances, preserve angle measures, preserve lengths, while a dilation is not a rigid transformation.

As you can see very clearly, it is not preserving lengths. It is not, for example, preserving the radius of the circle. In order for two figures to be congruent, the mapping has to be only with rigid transformations. Because she used a dilation, in fact, you have to use a dilation if you wanna be able to map M onto N because they have different radii, then she's not correct. These are not congruent figures. She cannot make this conclusion.

More Articles

View All
Secant line with arbitrary difference (with simplification) | AP Calculus AB | Khan Academy
A secant line intersects the curve ( y ) is equal to ( 2x^2 + 1 ) at two points with ( x ) coordinates ( 4 ) and ( 4 + h ), where ( h ) does not equal zero. What is the slope of the secant line in terms of ( h )? Your answer must be fully expanded and sim…
Lewis diagrams for molecules | Chemistry | Khan Academy
Let’s draw LS draw structures for certain molecules. It’s a lot of fun to do that. Okay, now the first thing we need to do to draw these structures is to identify the number of valence electrons. Okay, and we’ve talked about these valence electrons in ou…
What is a pronoun? | The parts of speech | Grammar | Khan Academy
Hello grammarians! We’re going to start talking about pronouns today, and of course that begins with the question: What are pronouns? Allow me to answer that question by way of a demonstration. Emma laughed so hard, milk came out of Emma’s nose. Zach lif…
The Global Economic Trends Post-Election | Explorer
Where do you see things now that we’re about a month in? I would actually distinguish between what we actually see in the markets and the story that Wall Street is telling. The story that Wall Street is telling is all optimistic. We’re going to have all …
How to Be a Great Founder with Reid Hoffman (How to Start a Startup 2014: Lecture 13)
So when I looked through the syllabus to this class and thought about what I could possibly add that would be useful in addition to the very skills, one of the things I’ve been thinking about has been how do you think about yourself as a founder? How do y…
The Most Advanced Civilization In The Universe
[Music] Earth and civilization, as we know it, has come a long way in the past 200,000 years and has experienced a multitude of changes. In that time, the human species has only existed for a mere 0.0015 percent of the immense 13.7 billion-year age of the…