Question

given: ij = kj
prove: il ≠ lm (using the
indirect method)

1. ij = kj
2. given
3. either il = lm or

il ≠ lm. assume
il = lm.

1. a statement is either

true or false.

1. click here to insert
2. base angles theorem
3. m∠1 > m∠k
4. click here to insert
5. click here to insert
6. substitution property

of inequality

Explanation:

Step1: Apply Base Angles Theorem

If \(IL = LM\), then \(\angle2=\angle1\) (Base Angles Theorem states that in an isosceles triangle, the base angles are equal).

Step2: Use Exterior Angle Inequality

\(m\angle2>m\angle K\) (Exterior Angle Inequality: An exterior angle of a triangle is greater than any non - adjacent interior angle. In \(\triangle IK M\), \(\angle2\) is an exterior angle and \(\angle K\) is a non - adjacent interior angle).

Step3: Substitute

Since \(\angle2=\angle1\) (from Step 1) and \(m\angle2>m\angle K\) (from Step 2), by substitution \(m\angle1>m\angle K\)

Answer:

1. \(\angle2 = \angle1\)
2. Exterior Angle Inequality
3. \(m\angle2>m\angle K\)