Question

peter is walking home from school. on his way home, he stops by a park and stays their for a bit. suddenly, he remembers that he has to get home for his sisters birthday party. peter then leaves the park and sprints the rest of the way. sketch a graph of this.

triangle abc is a reflection of the scalene triangle xyz. select all statements that must be true.

question 26
question 27

Explanation:

• When two figures are reflections of each other (a type of congruence transformation), their corresponding angles and corresponding sides are equal.
• For triangle \(XYZ\) and its reflection \(ABC\):
• Corresponding angles: \(\angle Z\) corresponds to \(\angle C\), \(\angle X\) corresponds to \(\angle A\), \(\angle Y\) corresponds to \(\angle B\).
• Corresponding sides: \(\overline{YZ}\) corresponds to \(\overline{BC}\), \(\overline{XZ}\) corresponds to \(\overline{AC}\), \(\overline{XY}\) corresponds to \(\overline{AB}\).

Answer:

a) \(m\angle Z = m\angle C\) (because they are corresponding angles in congruent triangles formed by reflection); e) \(\overline{XZ}=\overline{AC}\) (because they are corresponding sides in congruent triangles formed by reflection)