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Theorem 7.6 : If two sides of a triangle...

Theorem 7.6 : If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater)

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To prove Theorem 7.6: If two sides of a triangle are unequal, the angle opposite to the longer side is larger, we will follow these steps: ### Step-by-Step Solution: 1. **Consider a Triangle**: Let triangle ABC be given such that \( AB > AC \). We need to prove that \( \angle C > \angle B \). 2. **Construct a Point**: Construct a point P on line AB such that \( AP = AC \). Join point C to point P, forming triangle APC. ...
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In a triangle the greater angle has the longer side opposite to it.

Fill in the blanks to make the following statements true: In a right triangle the hypotenuse is the ...... side. The sum of three altitudes of a triangle is ......... than its perimeter. The sum of any two sides of a triangle is ......... than the third side. If two angles of a triangle are unequal, then the smaller angle has the ........... side opposite to it. Difference of any two sides of a triangle is ......... than the third side. If two sides of a triangle are unequal, then the larger side has ..... angle opposite to it.

Knowledge Check

  • The lengths of two sides of a triangle are 50 inches and 63 inches. The angle opposite the 63-inch side is 66^(@) . How many degrees are in largest angle of the triangle ?

    A
    `66^(@)`
    B
    `67^(@)`
    C
    `68^(@)`
    D
    `71^(@)`

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