Is there a triangle with sides 1, 6, 7? Why? 2. The angles of a triangle are related as 1: 2: 6. Find the angles.

1. Is there a triangle with sides 1, 6, 7? Why? 2. The angles of a triangle are related as 1: 2: 6. Find the angles. 3. The outer angle at the apex of an isosceles triangle is 70 °. Find the corners at the base. Solve in two ways. 4. In an isosceles triangle ABC with a base AC, the angle B is equal to 64 °. Find the angle AMC, where CM is the bisector of angle C. 5. The two sides of an isosceles triangle are 13 and 15. What size can the third side be? 6. An arbitrary 4-gon АВСК is given. Prove that AB + BC + CK & gt; AK 7. Is there a triangle with angles of 15, 126, 40 degrees? 8. In a triangle with a perimeter of 54, one of the sides is 1 cm smaller than the other and 4 cm larger than the third. Find the sides of the triangle.

1. A triangle exists only if the sum of any two of its sides is greater than the third side (7 + 1> 6, 6 + 1 = 7, 7 + 6> 1) -> such a triangle exists
2.X + 2x + 6x = 180 (the sum of angles in any triangle is 180 degrees) 9x = 180 x = 180/9 x = 20 To find a larger angle, 6 * 20 = 120 To find the average angle, 2 * 20 = 40 For finding a smaller angle is necessary 1 * 20 = 20
3. The sum of the angles in any triangle is 180 degrees. The angles in an isosceles triangle are equal at the base, which means: (180-70) / 2 = 55 Answer: the angle at the base is 55 degrees
4. Let half of the angle cut off by the bisector be x, then the angle at the base C will be 2x Also from the properties of the corners of the track we obtain 2x + 2x + 64 = 180 4x = 180-64 4x = 116x = 116: 4x = 29 – AFM angle 29 * 2 = 58 – MAC angle 180- (58 + 29) = 93 – AMC angle