Chapter Test
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Begin by labeling the vertices with their coordinates.
See solution.
Let's mark the coordinates of the unlabeled vertices.
Since SAS only requires us to calculate two sides in each of the triangles, we will use this theorem.
| Side | Points | sqrt((x_2-x_1)^2+(y_2-y_1)^2) | d |
|---|---|---|---|
| PR | ( 12,15), ( 3,30) | sqrt(( 12- 3)^2+( 15- 30)^2) | sqrt(306) |
| RQ | ( 21,30), ( 12,15) | sqrt(( 21- 12)^2+( 30- 15)^2) | sqrt(306) |
| TR | ( 12,15), ( 3,0) | sqrt(( 12- 3)^2+( 15- 0)^2) | sqrt(306) |
| SR | ( 21,0), ( 12,15) | sqrt(( 21- 12)^2+( 0- 15)^2) | sqrt(306) |
Both triangles are isosceles triangles with congruent legs. As we already stated, the included angle of the triangles legs are vertical angles and therefore congruent. Therefore, we can by the SAS Congruence Theorem claim that the triangles are congruent.
