standard_description: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
problem_activity: Task
Below is an isosceles triangle $ABC$ with $|AB| = |AC|$:
[IMG]
Three students propose different arguments for why $m(\angle B) = m(\angle C)$.
Ravi says
If I draw the bisector of $\angle A$ then this is a line of symmetry for $\triangle ABC$ and so $m(\angle B) = m(\angle C)$.
Brittney says
If $M$ is the midpoint of $\overline{BC}$ then $\triangle ABM$ is congruent to $\triangle ACM$ and so $\angle B$ and $\angle C$ are congruent.
Courtney says
If $P$ is a point on $\overline{BC}$ such that $\overleftrightarrow{AP}$ is perpendicular to $\overline{BC}$ then $\triangle ABP$ is congruent to $\triangle ACP$ and so $\angle B$ and $\angle C$ are congruent.
Fill in the details in each argument to show why $m(\angle B) = m(\angle C)$. Can you find another different argument showing that $m(\angle B) = m(\angle C)$?


aligns: no