Questions: True or false? In the triangle below, side LM is parallel to side γχ.

Transcript text: True or false? In the triangle below, side $\overline{L M}$ is parallel to side $\overline{\gamma \chi}$

Solution

Solution Steps

Step 1: Identify the Given Information

The problem states that in triangle $ ZYX $, side $ LM $ is parallel to side $ YX $. We need to determine if this statement is true or false.

Step 2: Analyze the Diagram

In the diagram, $ ZL $ and $ ZM $ are drawn such that $ L $ and $ M $ are points on $ ZY $ and $ ZX $ respectively. The markings on the diagram indicate that $ ZL $ is equal to $ LY $ and $ ZM $ is equal to $ MX $.

Step 3: Apply the Midsegment Theorem

The Midsegment Theorem states that a segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long. Since $ L $ and $ M $ are midpoints of $ ZY $ and $ ZX $ respectively, $ LM $ is parallel to $ YX $.

Final Answer

True

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