Question 1

The figure shows line $r$, points $P$ and $T$ on line $r$, and point $Q$ not on line $r$. Also shown is ray $PQ$.

Consider the partial construction of a line parallel to $r$ through point $Q$. What would be the final step in the construction?

Accepted Answer

draw a line through $Q$ and $S$

Answer

draw a line through $T$ and $S$

Answer

draw a line through $W$ and $S$

Answer

draw a line through $P$ and $S$

Question 2

The figure shows line $r$, points $P$ and $T$ on line $r$, and point $Q$ not on line $r$. Also shown is ray $PQ$.

Once the construction is complete, which of the reasons listed contribute to proving the validity of the construction?

Accepted Answer

When two lines are cut by a transversal and the corresponding angles are
congruent, the lines are parallel.

Answer

definition of segment bisector

Answer

When two lines are cut by a transversal and the vertical angles are
congruent, the lines are parallel.

Answer

definition of an angle bisector

Question 3

Triangle $ABC$ has vertices at $A(1 ,2), B(4,6),$ and $C(4,2)$ in the coordinate plane. The triangle will be reflected over the $x	ext{-axis}$ and then rotated $180^\circ$ about the origin to form $\vartriangle A'B'C'$. What are the vertices of $\vartriangle A'B'C'$?

Accepted Answer

$A'(-1, 2) , B'(-4, 6), C'(-4, 2)$

Answer

$A'(1, -2) , B'(4, -6), C'(4, -2)$

Answer

$A'(1, 2) , B'(4, 6), C'(4, 2)$

Answer

$A'(-1, -2) , B'(-4, -6), C'(-4, -2)$

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