Define and prove the Pythagorean theorem. Use the Pythagorean theorem and its converse in the solution of problems.
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Given the subdivided right triangle below, show that $${a^2+b^2=c^2}$$.
Geometry > Module 2 > Topic D > Lesson 24 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Find $${RS}$$.
8.3 Using Similar Right Triangles is made available by CK-12 under the CC BY-NC 3.0 license. © CK-12 Foundation 2017. Visit them at ck12.org. Accessed Feb. 28, 2018, 11:10 a.m..
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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In each row in the table below are the lengths of the legs and hypotenuse of different right triangles. Find the missing side lengths in each row in simplest radical form.
$${\mathrm{Leg}_1}$$ | $${\mathrm{Leg}_2}$$ | Hypotenuse |
15 | 25 | |
15 | 36 | |
3 | 7 | |
100 | 200 |
Geometry > Module 2 > Topic D > Lesson 24 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
In right triangle $${ABC}$$ with $${\angle C}$$ a right angle, an altitude of length $$h$$ is dropped to side $${\overline{AB}}$$ into segments of length $$x$$ and $$y$$. Use the Pythagorean theorem to show $$h^2=xy$$.
Geometry > Module 2 > Topic D > Lesson 24 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..