Download File

Geometry
Name:
Period:
Date:
Warm Up 3/5
Lesson 5-7: The Pythagorean Theorem II
Objectives
Students will…
-
Be able to know what the Converse of the Pythagorean Theorem says.
Be able to set up and apply Pythagorean Inequalities to classify triangles.
Triangles
Recall that triangle is any ____________-sided polygon with three interior angles. With regards to the sides, the
following notations are commonly used:
is the ________________, or the longest side, while
and
are the ______________.
The Converse Pythagorean Theorem
We not only revisited, but proved the Pythagorean Theorem during the last lesson. Well, it turns out that
Pythagorean Theorem is actually __________________ (if and only if).
Converse of the Pythagorean Theorem- For any triangle that has side lengths, with c being the length of its
hypotenuse, and a and b representing the length of its two shorter legs, such that
, then it is a
_____________ triangle.
Ex.
For
, if
, then
is a right triangle.
The proof of the converse is a little more difficult than the Pythagorean Theorem, so we won’t do it in this class.
Example
Find the value of x. Give your answer in simplest radical form.
Find the value of x. Give your answer in simplest radical form.
1
Geometry
Name:
Period:
Date:
Pythagorean Inequalities Theorem
There is another useful application to the Pythagorean Theorem. It is used to ________________ triangles (acute,
obtuse, or right).
Pythagorean Inequalities Theorem- For any triangle with side lengths,
and with being the hypotenuse,
we have the following:
If
, then the triangle is ______________. (___________________________________)
If
, then the triangle is ______________.
If
, then the triangle is ______________.
Classifying Triangles
Classify the triangle that has side lengths
as acute, obtuse, or right.
Classify the triangle that has side lengths
as acute, obtuse, or right.
Classify the triangle that has side lengths
as acute, obtuse, or right.
Classify the triangle that has side lengths
√ as acute, obtuse, or right.
In Closing/Exit Ticket
Take a moment to write down the Converse of the Pythagorean Theorem.
Exit TicketTake a moment to write how you classify triangles as acute, obtuse, or right using the Pythagorean Inequalities
Theorem. Then, compare your answers with a partner.
This is your exit ticket! You may not leave until you finish this.
Homework 3/5
Converse of Pythagorean Theorem WKSHT
2