ESSENTIAL QUESTION What kind of triangle is there

The Converse of the Pythagorean Theorem l If the square of the length of

Example 1 Verify a Right Triangle Is ∆ABC a right triangle? SOLUTION c 2

Right Triangle? ? 2 lc = 2 a + 2 b RIGHT 2 lc

I DO…. Example 2 Show that the triangle is an acute triangle. SOLUTION Compare

I DO…. Example 3 Show that the triangle is an obtuse triangle. SOLUTION Compare

Example 4 WE DO…. Classify the triangle as acute, right, or obtuse. SOLUTION c

Example 5 WE DO. … Classify the triangle with the given side lengths as

Checkpoint YOU DO…. Classify the triangle as acute, right, or obtuse. Explain. 1. 2.

Checkpoint Classify Triangles Classify the triangle as acute, right, or obtuse. Explain. 1. 2.

Checkpoint Classify Triangles Use the side lengths to classify the triangle as acute, right,

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ESSENTIAL QUESTION: What kind of triangle is there 2 when c is not equal to 2 2 a +b

The Converse of the Pythagorean Theorem l If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Example 1 Verify a Right Triangle Is ∆ABC a right triangle? SOLUTION c 2 =? a 2 + b 2 202 =? 122 + 162 400 =? 144 + 256 400 = 400 ANSWER Compare c 2 with a 2 + b 2. Substitute 20 for c, 12 for a, and 16 for b. Multiply. Simplify. It is true that c 2 = a 2 + b 2. So, ∆ABC is a right triangle.

Right Triangle? ? 2 lc = 2 a + 2 b RIGHT 2 lc > 2 a + 2 b OBTUSE lc 2 < a 2 + b 2 ACUTE

I DO…. Example 2 Show that the triangle is an acute triangle. SOLUTION Compare the side lengths. c 2 =? a 2 + b 2 ? 35 2 = 42 + 52 35 =? 16 + 25 35 < 41 ANSWER Compare c 2 with a 2 + b 2. Substitute 35 for c, 4 for a, and 5 for b. Multiply. Simplify. Because c 2 < a 2 + b 2, the triangle is acute.

I DO…. Example 3 Show that the triangle is an obtuse triangle. SOLUTION Compare the side lengths. c 2 =? a 2 + b 2 225 =? 64 + 144 225 > 208 ANSWER Multiply. Simplify. Because c 2 > a 2 + b 2, the triangle is obtuse.

Example 4 WE DO…. Classify the triangle as acute, right, or obtuse. SOLUTION c 2 =? a 2 + b 2 82 =? 52 + 62 64 =? 25 + 36 64 > 61 ANSWER Multiply. Simplify. Because c 2 > a 2 + b 2, the triangle is obtuse.

Example 5 WE DO. … Classify the triangle with the given side lengths as acute, right, or obtuse. a. 4, 6, 7 b. 12, 35, 37 SOLUTION a. c 2 =? a 2 + b 2 b. c 2 =? a 2 + b 2 72 =? 42 + 62 372 =? 122 + 352 49 =? 16 + 36 1369 =? 144 + 1225 49 < 52 1369 = 1369 The triangle is acute. The triangle is right.

Checkpoint YOU DO…. Classify the triangle as acute, right, or obtuse. Explain. 1. 2. 3.

Checkpoint Classify Triangles Classify the triangle as acute, right, or obtuse. Explain. 1. 2. 3. ANSWER obtuse; 62 > 22 + 52 ANSWER right; 172 = 82 + 152 ANSWER acute; 72 < 72 + 72

Checkpoint Classify Triangles Use the side lengths to classify the triangle as acute, right, or obtuse. 4. 7, 24 5. 7, 24, 25 6. 7, 24, 26

Checkpoint Classify Triangles Use the side lengths to classify the triangle as acute, right, or obtuse. 4. 7, 24 ANSWER acute 5. 7, 24, 25 ANSWER right 6. 7, 24, 26 ANSWER obtuse

l Hw Practice 4. 5 B