This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
8 cm, PQ = 6 cm, and .
Right rebbecajoseph36, let's go.
Here are the steps to construct the triangles:
1. Construct a triangle PQR such that PR = 8 cm, PQ = 6 cm, and .
Step 1: Draw a line segment of length . Step 2: At point , construct a perpendicular line (an angle of ) to . Step 3: Along the perpendicular line from , measure and mark a point such that . Step 4: Join points and with a straight line segment. The triangle is now constructed.
2. Construct a triangle ABC such that AB = 6.5 cm, BC = 5 cm, and AC = 5 cm.
Step 1: Draw a line segment of length . Step 2: With as the center, draw an arc with a radius of (since ). Step 3: With as the center, draw another arc with a radius of (since ). Step 4: The point where the two arcs intersect is point . Step 5: Join points to and to with straight line segments. The triangle is now constructed.
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Right rebbecajoseph36, let's go. Here are the steps to construct the triangles: 1.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.