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1试题呈现(安徽卷第23题)如图1,A、B分别在射线OM、ON上,且∠MON为钝角,现以线段OA、OB为斜边向∠MON的外侧作等腰直角三角形,分别是△OAP、△OBQ,点C、D、E分别是OA、OB、AB的中点。(1)求证:△PCE≌△EDQ;(2)延长PC、QD交于点R。①如图2,若∠MON=150°,求证:△ABR为等边三角形;②如图3,若△ARB∽△PEQ,求∠MON大小和
1 questions presented (Anhui volume 23 questions) as shown in Figure 1, A, B, respectively, in the beam OM, ON, and ∠ MON is an obtuse angle, now the line segment OA, OB oblique hypotenuse ∠ MON outside of the isosceles right triangle , Respectively △ OAP, △ OBQ, points C, D, E are the midpoint of OA, OB, AB. (1) Confirmation: △ PCE≌ △ EDQ; (2) extend the PC, QD at the point R. ① as shown in Figure 2, if ∠MON = 150 °, verify: △ ABR equilateral triangle; ② as shown in Figure 3, if △ ARB∽ △ PEQ, find ∠MON size and