Question

problem 23
clear
exit
given: ( mangle5 = mangle6 )
prove: ( ec>ae )

1. click here to insert
2. given
3. ( mangle5>mangle c )
4. click here to insert
5. click here to insert
6. click here to insert
7. ( ec>ae )
8. click here to insert

Explanation:

Step1: Insert the given statement

\(m\angle5 = m\angle6\)

Step2: State the exterior angle theorem reason

An exterior angle of a triangle is greater than any non - adjacent interior angle. For \(\triangle BEC\), \(\angle5\) is an exterior angle and \(\angle C\) is a non - adjacent interior angle.

Step3: Substitute \(m\angle6\) for \(m\angle5\)

\(m\angle6>m\angle C\)

Step4: State the side - angle relationship reason

In a triangle, the side opposite the larger angle is longer. In \(\triangle AEC\), since \(m\angle6>m\angle C\), the side opposite \(\angle6\) is \(EC\) and the side opposite \(\angle C\) is \(AE\).

Answer:

1. \(m\angle5 = m\angle6\)
2. An exterior angle of a triangle is greater than any non - adjacent interior angle
3. \(m\angle6>m\angle C\)
4. In a triangle, the side opposite the larger angle is longer