TODAY IN GEOMETRY…

Warm Up: Simplifying Radicals

Practice: Solving missing sides using the Pythagorean Theorem

Learning Target : Use the Converse of the Pythagorean Theorem determine if a triangle is a right triangle

Independent Practice

WARMUP: MULTIPLYING AND SIMPLIFYING RADICALS:

1. 2.

3.

4. 5.

6.

¿5+6 ¿ 4√20¿𝟏𝟏

Perfect Squares:

149

162536496481

100121144

REVIEW:

USING THE PYTHAGOREAN THEOREM TO FIND MISSING

SIDES

32

17𝑥

PRACTICE: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in the simplest radical form.

The unknown side is not attached to the right angle so it is a hypotenuse of the triangle.

Use the Pythagorean theorem to find the missing leg:

𝑥58

26

PRACTICE: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in the simplest radical form.

The unknown side is attached to the right angle so it is a leg of the triangle.

Use the Pythagorean theorem to find the missing leg:

6

8

12

𝑥

PRACTICE: Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in the simplest radical form.

The unknown side is not attached to the right angle so it is a hypotenuse of the triangle.(There are two right triangles. You must find a before you can find x.)Use the Pythagorean theorem to find a:

𝑎

Use the Pythagorean theorem again to find x:

¿10

CONVERSE TO THE PYTHAGOREAN THEOREM:

3 PARTS!!!

PART 1:

RIGHT TRIANGLE if…

𝑎2+𝑏2=𝑐2

PART 2:

ACUTE TRIANGLE if…

PART 3:

OBTUSE TRIANGLE if…

𝑎2+𝑏2>𝑐2𝑎2+𝑏2<𝑐2

CONVERSE TO THE PYTHAGOREAN THEOREM: 𝑎 𝑐

𝑏

𝐵

𝐴𝐶

8

4 43

PRACTICE: Tell whether a triangle with the given side lengths is a right triangle. Assign the given lengths to the sides of

the triangle. The largest side is always assigned the hypotenuse!

Use the Pythagorean theorem to check if it is a right triangle.

? ? ? NOT A RIGHT ANGLE!

TRIANGLE IS OBTUSE!

4 ,43 ,8

4 8

43

11

10 14

PRACTICE: Tell whether a triangle with the given side lengths is a right triangle. Assign the given lengths to the sides of

the triangle. The largest side is always assigned the hypotenuse!

Use the Pythagorean theorem to check if it is a right triangle.

? ? ? NOT A RIGHT ANGLE!

TRIANGLE IS ACUTE!

10 ,11 ,14

10 11

14

5.2

4.3 6.1

PRACTICE: What kind of triangle (acute, obtuse or right) can be formed with segment lengths

Assign the given lengths to the sides of the triangle. The largest side is always assigned the hypotenuse!

Use the Pythagorean theorem to check if it is a right triangle.

? ? ? NOT A RIGHT ANGLE!

TRIANGLE IS ACUTE!

4.3 5.2

6.1

PRACTICE: Graph points . Connect the points to form . Decide whether the triangle is acute, right or obtuse.

𝐴 (−2 ,4 )𝐵 (6 ,0 )𝐶 (−5 ,−2)

𝑨

𝑩

𝑪

Use the distance formula to find the segment lengths:

Use the Pythagorean theorem to check if it is a right triangle.

? ? ? IT IS A RIGHT TRIANGLE!

HOMEWORK #2:

Pg. 444:1-6, 8, 10, 12

If finished, work on other assignments:

HW #1: Pg. 436: 3-29 odd