今年三月,我校八年级数学备课组进行了一次阶段性目标达成检测,有一道证明题如下:如图,在四边形ABCD中,BD平分∠ABC,AC⊥BD于R,PQ与BC、AD分别相交于点Q、P,且∠BAD=∠BQP,求证:QP∥CD(本题满分7分)提供的评分标准:证明:∵BD平分∠ABC,AC⊥BD于R,∴∠ABR=∠CBR,∠ARB=∠BRC=90°.第一逻辑段又∵BR=BR,∴△ABR≌△CBR.∴BC=AB…………………………3 In March of this year, the eighth grade mathematics lesson preparation group of our school conducted a milestone test. There is a proof question as follows: In the quadrilateral ABCD, BD is divided into ∠ABC, AC ⊥ BD in R, PQ and BC, AD Respectively, intersect at point Q, P, and ∠BAD = ∠BQP, verify: QP∥CD (7 out of 7 points) to provide the grading criteria: Prove: ∵BD bisect ∠ABC, AC ⊥ BD in R, ∴∠ABR = ∠ CBR, ∠ARB = ∠BRC = 90 °. The first logical segment 又BR = BR, ∴ΔABR≌ΔCBR.∴BC = AB .............................. 3