Chapter 14.2A, Problem 5A

Assessment 14-2A

a. Refer to the following figure and suppose lines $l$ and $m$ are parallel and $\Delta ABC$ is reflected in $l$ to obtain $\Delta A^{\prime }{B}^{\prime }{C}^{\prime }$ and then $\Delta A^{\prime }{B}^{\prime }{C}^{\prime }$ is reflected in $m$ to obtain $\Delta A^{″}{B}^{″}{C}^{″}$. Determine whether the same final image is obtained if $\Delta ABC$ is reflected first in $m$ and then its image is reflected in $l$.

b. Conjecture what single transformation will take $\Delta ABC$ directly to $\Delta A^{″}{B}^{″}{C}^{″}$. Check your conjecture using tracing paper.