Similar Triangles Pythagorean Theorem

1. Similar Triangles Pythagorean Theorem

2. Similar Triangles Triangles that have the same shape, but not necessarily the same size, are called similar triangles. Two triangles ABC and DEF are similar if • their corresponding angles are equal 2) their sides are proportional Similarity is found in scale models, blueprints, maps, microscopes, and when enlaraging or reducing a photocopy. All of the angles are exactly the same size, so the object looks exactly like the original, only larger or smaller.

3. Exercises • Find missing length. 2) Triangles ABC and DEF are similar. Find the two sides of triangle ABC.

4. Exercises 3) Find the height of the tower. 4) The height of the house can be found by comparing its shadow cast by 3ft stick. Find the height of the house.

5. Pythagorean Theorem This theorem applies only to right triangles. The opposite side of a right triangle, which is also the longest side in the triangle, is called the hypotenuse. The other two sides are called legs. The legs form the right angle Pythagorean Theorem: (hypotenuse) 2 = (leg)2 + (leg)2 For any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs of the triangle.

6. If c is the length of the hypotenuse of a right triangle, and a and b are the length of the other two sides then c2 = a2 + b2 This theorem provides a simple relation between the three sides of a right triangle – if the lengths of two sides of a right triangle are known, it allows the easy calculation of the third side.

7. Exercises • Find the unknown length in each right triangle. c) a) b) d) e)

8. Exercises 2. What is the length of AB in the accompanying figure? • A rectangular field is 75 meters wide and 100 meters long. • What is the length of a diagonal path connecting two opposite corners ?