Question

Which statements are true about triangle PQR? Check all that apply.

The length of side PQ is 5 units.
The length of side QR is 5 units.
The length of side RP is 5 units.
PQR is an equilateral triangle.
PQR is an isosceles triangle.
PQR is a scalene triangle.

Answer 1

I don’t have the diagram or side/coordinate information for triangle PQR, so I can’t tell which statements are true. Please either upload the figure or give the coordinates/side lengths.

How you (or I) can determine each statement:
- Find the three side lengths PQ, QR, RP. If you have coordinates P(x1,y1), Q(x2,y2), R(x3,y3), use the distance formula:
- PQ = sqrt((x2−x1)^2 + (y2−y1)^2), etc.
- Compare the lengths:
- If PQ = 5 then the first statement is true; similarly for QR = 5 and RP = 5.
- If all three side lengths are equal, PQR is equilateral (and therefore also isosceles).
- If exactly two side lengths are equal, PQR is isosceles (but not equilateral).
- If all three side lengths are different, PQR is scalene.

If you share the picture or the coordinates/measurements, I’ll compute the distances and mark which statements are true.