Your goal is to use the manipulative below to explore and understand the Converse of the Pythagorean Theorem and its corollaries. Recall: a corollary is something that is easily proven from something else. The Pythagorean Theorem can be used for more than just right triangles. Who knew?
The Pythagorean Theorem states: "If you have a right triangle, then [math]a^2+b^2=c^2[/math]". What should the converse of this statement be? Write it out in one complete conditional statement.
Using the sliders in the manipulative above, create a right triangle, compute the values [math]a^2+b^2[/math] and [math]c^2[/math] and record these values in the google doc below. You will record all future values here, so keep the google doc open.
https://docs.google.com/spreadsheets/d/1NDY7pzbdz8PTeMIjnkC8jQA2qu78sVJ-XaTErwV4-Q0/copy[br][br]Copy and paste the above link to another tab in your browser.[br]
Fill in the blank: When you have a [b]right[/b] triangle, [math]c^2[/math] ______ [math]a^2+b^2[/math].
Now, using the same manipulative as in step 1, use the sliders to create three different acute triangles. Note the a, b, and c values in your google spreadsheet and then compute the [math]c^2[/math] and [math]a^2+b^2[/math] values.
Fill in the blank: When you have an [b]acute[/b] triangle, [math]c^2[/math] _____ [math]a^2+b^2[/math].
Now, using the same manipulative as in step 1, use the sliders to create three different obtuse triangles. Note the a, b, and c values in your google spreadsheet and then compute the [math]c^2[/math] and [math]a^2+b^2[/math] values.
Fill in the blank: When you have an [b]obtuse[/b] triangle, [math]c^2[/math] _____ [math]a^2+b^2[/math].
Use the relationships you recognized above to classify the following triangles.
Classify the triangle above as right, obtuse, or acute. Show all work in the box below. You may use a^2 to represent [math]a^2[/math].
The above triangle is ________.
Classify the triangle above as right, obtuse, or acute. Show all work in the box below.
The above triangle is _______.
Classify the triangle above as right, obtuse, or acute. Show all work in the box below.
The above triangle is _______.