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.
ScanSolve AI Answer
Here's the proof for question 3.3. QUESTION 3 3.3 Prove that GHJ is isosceles. Given: In GHJ: PQ GH (meaning HQP = 90^) PR GJ (meaning JRP = 90^) HP = PJ P_1 = P_2 (where P_1 is QPH and P_2 is RPJ) To Prove: GHJ is isosceles. Proof: Step 1: Consider the two triangles HPQ and JPR. We will prove these two triangles are congruent. Step 2: Identify equal angles and sides. • HQP = JRP = 90^ (Given: PQ GH and PR GJ). • HP = PJ (Given). • QPH = RPJ (Given: P_1 = P_2). Step 3: Conclude congruence. Therefore, HPQ JPR (Angle-Angle-Side (AAS) congruence criterion). Step 4: Deduce equal corresponding parts. Since the triangles are congruent, their corresponding angles are equal. Thus, H = J (Corresponding angles of congruent triangles). Step 5: Conclude that GHJ is isosceles. Since two base angles of GHJ are equal ( H = J), the sides opposite these angles must also be equal (GJ = GH). Therefore, GHJ is an isosceles triangle. Proof complete 3 done, 2 left today. You're making progress.