5. Complete the following proof. Given: the figure where R is the midpoint of PT and QS Prove: APQR = ATSR R Statements Reasons 1. PQ 1QS, QS 1 ST, PQ = ST; R is the midpoint of PT and QS. 1. 2. definition of midpoint 2. 3. ZQ and LS are right angles. 4. All right angles are congruent. 5. 5. ZPRQ = ZTRS 6. AA→ AAA 6. 7.. 7. ΔΡΟR= ΔTR CHA 3. 4.

hat re- and the 3. The * 7. Suppose that in a trapezoid ABCD, as in Figure 12.74, AB and CD are parallel. A D E C B Figure 12.74 Trapezoid and the triangles formed by its diagonals. Let E be the point where the diagonals AC and BD meet. Explain why triangles AED and BEC must have the same area. (Do this without meas- uring actual lengths or areas.)

Mr. Williams had this proof on the board. Which definition or theorem justifies step 2, zADC and zABC are both right angles? Given: Circle A with tangents BC and DC Prove: Arc BE - Arc DE A Statements 1. Circle A with tangents BC and DC 2. ADC and ABC are both right, Reasons 1. 2. angles 3. AD = AB 3. 4. AC AC 4. 5. AABC = AADC - ΔADC 5. 6. DAC = BAC 6. 7. Arc BE = Arc DE 7. О СРСТС O Reflexive property

What other information has to be true in order to prove PQR is congruent to PSR by Side angle Side