Question

list all the pairs of congruent angles write the ratio of the corresponding sides in a statement of proportionality find the value of x

Answer 1

Solution

The pair of congruent sides are

$\begin{gathered} PR\cong AC \\ RQ\cong CB \\ PQ\cong AB \end{gathered}$

The ratio of corresponding sides in a statement are

$\frac{PR}{AC}=\frac{RQ}{CB}=\frac{PQ}{AB}$

PQ = 21

AB = x

RQ=24

CB=20

Hence substituting these in x is given as

$\begin{gathered} \frac{24}{20}=\frac{21}{x} \\ 24x\text{ = 21}\times20 \\ x=\frac{420}{24} \\ x\text{ =}17.5 \end{gathered}$

Hence x = 17.5