Question

Wich of the following is true if abc~apt select all that apply

Answer 1

Use the fact that the triangles ABC and QPR are similar to find the length of RP as well as the measure of the angles in the options.

Notice that AB and QP are corresponding sides, as well as RP and CB. Then:

`\begin{gathered} (AB)/(QP)=(CB)/(RP) \\ \Rightarrow(10)/(5)=(9)/(RP) \\ \Rightarrow2=(9)/(RP) \end{gathered}`

Solve for RP:

`\begin{gathered} \Rightarrow RP=(9)/(2) \\ \Rightarrow RP=4.5 \end{gathered}`

Since the sum of the internal angles of every triangle must be equal to 180º, then:

`m\angle A+m\angle B+m\angle C=180`

Substitute m
`\begin{gathered} \Rightarrow63+m\angle B+81=180 \\ \Rightarrow m\angle B+144=180 \\ \Rightarrow m\angle B=180-144 \\ \Rightarrow m\angle B=36 \end{gathered}`Since R corresponds to the angle C, then its measure is equal to 81º.

Since Q corresponds to the angle A, then its measure is equal to 63º.

Since P corresponds to the angle B, then its measure is equal to 36º.

Therefore, the statements which are true are:

`\begin{gathered} m\angle R=81^(\circ) \\ RP=\text{4}.5 \\ m\angle Q=63^(\circ) \end{gathered}`