Question

quiz 4-1: classifying and solving for sides/angles in triangles
directions: if g is the mid - point of $overline{ab}$, classify each triangle by its angles and sides.

1. $\triangle cfe$: right scalene
2. $\triangle bec$: obtuse scalene
3. $\triangle bfg$: e. e.
4. $\triangle gaf$: obtuse scalene

Explanation:

Step1: Recall triangle - classification rules

Classify by angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral).

Step2: Analyze \(\triangle CFE\)

It has a right - angle, and all sides are of different lengths, so it is a right - scalene triangle.

Step3: Analyze \(\triangle BEC\)

It has an obtuse angle, and all sides are of different lengths, so it is an obtuse - scalene triangle.

Step4: Analyze \(\triangle BFG\)

Assume "E.E." means equilateral. All sides are equal (if the markings imply so), and all angles are \(60^{\circ}\) (acute), so it is an equilateral (acute) triangle.

Step5: Analyze \(\triangle GAF\)

It has an obtuse angle, and all sides are of different lengths, so it is an obtuse - scalene triangle.

Answer:

1. \(\triangle CFE\): Right - Scalene
2. \(\triangle BEC\): Obtuse - Scalene
3. \(\triangle BFG\): Equilateral (Acute)
4. \(\triangle GAF\): Obtuse - Scalene