Question

calculating measures of a dilation
triangle bcd was dilated using the rule $d_{q, \frac{1}{2}}$.
what are the values of the unknown measures?
$m\angle cbd = \square^\circ$
$cq = \square$
$bd = \square$

Explanation:

Step1: Find angle measure

Dilation preserves angles. $m\angle C'B'D' = m\angle CBD$. In $\triangle BCD$, $m\angle CBD = 180^\circ - 34^\circ - 51^\circ = 95^\circ$.

Step2: Calculate CQ

Dilation scale factor $k = \frac{1}{2}$. $CQ = 2 \times C'Q = 2 \times 3 = 6$.

Step3: Calculate B'D'

B'D' = $k \times BD = \frac{1}{2} \times 22 = 11$.

Answer:

95, 6, 11