Question

triangle parts

• 3 sides: line ______ that connect vertices
• 3 vertices: ______ where two sides meet
• 3 angles: pairs of intersecting ______

1. practice: using visual cues

fill in the blanks to describe how the parts of this triangle are related
triangle with vertices a, b, c

• side ___ is opposite angle a.
• side ___ is opposite angle b.
• side ___ is opposite angle c.

Explanation:

Step1: Recall Triangle Part Definitions

Sides of a triangle are line segments connecting vertices. Vertices are points where two sides meet. Angles are formed by pairs of intersecting sides (segments). For opposite sides/angles: In triangle \(ABC\), side opposite angle \(A\) is \(BC\) (opposite vertex \(A\)), opposite angle \(B\) is \(AC\) (opposite vertex \(B\)), opposite angle \(C\) is \(AB\) (opposite vertex \(C\)).

Step2: Fill in First Set of Blanks

• Sides: line \(\boldsymbol{\text{segments}}\) (connect vertices).
• Vertices: \(\boldsymbol{\text{points}}\) (where two sides meet).
• Angles: pairs of intersecting \(\boldsymbol{\text{sides (or segments)}}\).

Step3: Fill in Practice Blanks

• Side opposite angle \(A\): Angle \(A\) is at vertex \(A\), so opposite side is \(BC\) (between \(B\) and \(C\)).
• Side opposite angle \(B\): Angle \(B\) is at vertex \(B\), so opposite side is \(AC\) (between \(A\) and \(C\)).
• Side opposite angle \(C\): Angle \(C\) is at vertex \(C\), so opposite side is \(AB\) (between \(A\) and \(B\)).

Answer:

• 3 sides: line \(\boldsymbol{\text{segments}}\) that connect vertices
• 3 vertices: \(\boldsymbol{\text{points}}\) where two sides meet
• 3 angles: pairs of intersecting \(\boldsymbol{\text{sides (segments)}}\)

• Side \(\boldsymbol{BC}\) is opposite angle \(A\).
• Side \(\boldsymbol{AC}\) is opposite angle \(B\).
• Side \(\boldsymbol{AB}\) is opposite angle \(C\).