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Geometry 3 Level 1 If you put the three angles of a triangle together they make… A straight line QuickTime™ and a GIF decompressor are needed to see this picture. Another proof Fold point C to AB. The fold should be parallel to AB. Find x 62 x 64 x 54 Find x 4x 4x x x 180 x x Find x 4x 6x 180 x x Find x 4x x 30 x x Can you read French? Yes, we wanted all angles. Isosceles triangle Two angles are the same Two sides are the same i.e. AC = BC CABCBA Name the base angles BAB1 and BB1 A Find x 36 x Find x 36 Reason: Base 's isos x = 72 Here’s a hard one. Find the value of . if AB + BP = AQ +QB? is called beta • • • • • • • • 1. Extend line AB to a point called R. 2. Make BR equal in length to BP. 3. Since AB+BP = AQ+QB, you can prove that AR=AC. 4. Triangle BRP is an isosceles triangle with the big angle equal to 180 degrees —2 beta. 5. Thus, angle BRP has to equal beta. 6. If angle BRP=beta, then angle ACB also equals beta because line AP bisects angle A. 7. Therefore the two halves of the chevron formed by points A, R, P, and C are identical. 8. If angle C = beta and angle B=2 beta, then beta has to equal 40 degrees for the triangle ABC to add to 180 degrees. Angles in a quadrilateral 180 360 180 Find the angles in the quadrilateral 4x x 360 3x 2x 4x 3x 2x x 360 Find the angles in the quadrilateral 4x x 360 3x 2x 10x 360 x 36 Find the angles in the quadrilateral 144 36 108 360 72 10x 360 x 36 Find x Exterior angles Exterior angles Exterior angle Exterior angle equals the sum of the opposite interior angles. Find the value of x. x 70 50 Find the value of x. x = 70 + 50 = 120 70 50