3.4 Is It A Right Triangle? Pg. 13 Pythagorean Theorem Converse and Distance.

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3.4 Is It A Right Triangle? Pg. 13 Pythagorean Theorem Converse and Distance

3.4 – Is It A Right Triangle?_______________ Pythagorean Theorem Converse and Distance In lesson 3.3, you learned how to use the Pythagorean Theorem. Today you are going to use this information to find the length between two points on a graph. You are also going to determine if the triangle is acute, right, or obtuse.

3.24 – DISTANCE Use the Pythagorean theorem to find the following.

A B 7 3 d = d 2 58 = d = d 2

b. A(-6, 2)and B(-2, -3) A B 5 4 d = d 2 41 = d = d 2

c. A(-1, 2)and B(3, 4) A B 2 4 x = d 2 20 = d = d 2

Distance Formula: x 2 – x 1 y 2 – y 1

3.25 – DISTANCE FORMULA Find the distance between the two points. Simplify your square roots.

a. A(2, 4)and B(8, 19) = d = d = d 2 d =

b. A(-2, 3)and B(-8, 6) = d = d 2 45 = d 2 d =

c. A(-5, 2)and B(-2, -7) = d = d 2 90 = d 2 d =

3.26 – WHAT'S THE PATTERN? Use the tools you have developed to find the lengths of the missing sides of the triangles below. If you know a shortcut, share it with your team. Look for any patterns in the triangles as you solve. Are any triangles similar and multiples of others? Keep answers in exact form.

3.27 – PYTHAGOREAN TRIPLES

3.28 – EXTRA PRACTICE Find the area of the shapes using Pythagorean triples to help find the missing sides.

8 3 4

8

A = 100un 2

Right Triangle Acute Triangle Obtuse Triangle b a c b a c b a c

3.29 – TRIANGLE CLASSIFICATION For each set of numbers, determine if the triangle is acute, right, or obtuse. SHOW WORK!

a. 8, 15, 17 ACUTE, RIGHT, or OBTUSE

b. 3, 5, 7 ACUTE, RIGHT, or OBTUSE

c. 8, 10, 12 ACUTE, RIGHT, or OBTUSE

d. ACUTE, RIGHT, or OBTUSE

e. ACUTE, RIGHT, or OBTUSE

f. ACUTE, RIGHT, or OBTUSE