Question

1. identify 2 sets of parallel lines and 2 sets of perpendicular lines.

a) parallel lines
b) perpendicular lines
c) name of quadrilateral abed is
d) name of triangle bec is
e) name the types of angles below:
i) dab
ii) bec
iii) ifo

Explanation:

Step1: Identify parallel lines

Parallel lines are lines that never intersect. In the figure, $\overline{AB}\parallel\overline{DC}$ and $\overline{AD}\parallel\overline{BE}$.

Step2: Identify perpendicular lines

Perpendicular lines intersect at a right - angle. Here, $\overline{BE}\perp\overline{EC}$ and $\overline{AB}\perp\overline{BE}$.

Step3: Name the quadrilateral

Quadrilateral $ABED$ has one pair of parallel sides, so it is a trapezoid.

Step4: Name the triangle

Triangle $BEC$ has a right - angle at $\angle BEC$, so it is a right - triangle.

Step5: Classify the angles

• $\angle DAB$ is an obtuse angle (greater than 90° and less than 180°).
• $\angle BEC$ is a right - angle (equal to 90°).
• $\angle IFO$ (assuming $I$ and $O$ are points not clearly defined in the main figure, but if we consider the general angle - type classification), without more information, if it is less than 90°, it is an acute angle.

Answer:

a) Parallel lines: $\overline{AB}\parallel\overline{DC}$, $\overline{AD}\parallel\overline{BE}$
b) Perpendicular lines: $\overline{BE}\perp\overline{EC}$, $\overline{AB}\perp\overline{BE}$
c) Name of quadrilateral $ABED$ is trapezoid
d) Name of triangle $BEC$ is right - triangle
e) i) $\angle DAB$ is obtuse angle
ii) $\angle BEC$ is right - angle
iii) $\angle IFO$ (if acute) is acute angle