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Geometry: Chapter 4

Geometry: Chapter 4. 4.1: Apply Triangle Sum Properties. A triangle is a polygon with three sides. A triangle with vertices A, B, and C is called “triangle ABC ”. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 217.

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Geometry: Chapter 4

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  1. Geometry: Chapter 4 4.1: Apply Triangle Sum Properties

  2. A triangle is a polygon with three sides. A triangle with vertices A, B, and C is called “triangle ABC”. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 217.

  3. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 217.

  4. Ex. 1: Classify the triangle shown below by measuring its sides and angles. Image taken from: http://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Triangle-acute.svg/460px-Triangle-acute.svg.png

  5. Ex. 2: Classify triangle ABC by its sides and by its angles. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 218.

  6. Ex. 2: Classify triangle ABC by its sides and by its angles. Step 1: Use the distance formula to find the side lengths.

  7. ANGLES When the sides of a polygon are extended, other angles are formed. The original angles are the interior angles. The angles that form linear pairs with the interior angles are the exterior angles. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 218.

  8. Theorem 4.1: Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 1800.

  9. Theorem 4.2 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 220.

  10. Ex. 3. Find the mDEF. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 219.

  11. Ex. 3. Find the mDEF. Using the Exterior Angle Theorem (Theorem 4.2), I know that: 3x + 6= 80 + x 3x-x= 80-6 2x = 74 x = 37 mDEF = 3x + 6= 3(37)+ 6 = 1170

  12. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary.

  13. Ex. 4 The support for the skateboard ramp shown forms a right triangle. The measure of one acute angle in the triangle is five times the measure of the other. Find the measure of each acute angle. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 220.

  14. A Right Triangle has two legs and a hypotenuse. The side opposite the right angles is the hypotenuse of the angle.

  15. An Isosceles Triangle has two legs and a base. The two sides that are congruent are called the legs.

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