22. Given:PRPQ,SQSRProve:m1m2Proof:23. Given:EDDF;m1m2;Dis the midpointof CB;AEAF.Prove:ACABProof:24. Given:RS¬UWST¬WVRT¬UVProve:mSmWIndirect Proof:Step 1Assume mSmW.Step 2If mSmW, then either mSmWor mSmW.Case 1:If mSmW, then RTUVby theSAS Inequality.Case 2:If mSmW, then RSTUWVbySAS, and RTUVby CPCTC. ThusRTUV.Step 3Both cases contradict the given RTUV.Therefore, the assumption must be false,and the conclusion,mSmW, must betrue.25.As the door is opened wider, the angle formedincreases and the distance from the end of thedoor to the door frame increases.26.By the SAS Inequality Theorem, if the treestarted to lean, one of the angles of the triangleformed by the tree, the ground, and the stakewould change, and the side opposite that anglewould change as well. However, with the stake inthe ground and fixed to the tree, none of the sidesof the triangle can change length. Thus, none ofthe angles can change. This ensures that the treewill stay straight.
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