Name: Block: Honors Geometry: 6.12: Quadrilateral Problems – 4 1. In rectangle ABCD, AB = 16 and AD = 5. F is on AB and G on CD such that FG , BD , and AC all intersect at point O. Find [FOB] + [GOC]. (Pg. 241: 8.56) € 2. € € € In rectangle ABCD, M is the midpoint of BC . Point P and Q lie on AB and DC , respectively, such that PB = and m∠PMQ is a right angle. What is the ratio PM:MQ? (Pg. 241: 8.58) € 3. € € 4 BC 3 € In the diagram, ABCD is a parallelogram and E is on the extension of BC past C. AE and CD meet at point F. Given [ADF] = 64 and [CEF] = 4, determine the following: (Pg. 242: 8.59) (a) € € CF DF (b) [BFC] (c) [ABCD] € € € 4. Remember this problem we did in class? The large square had a side length of X and in class we drew four lines that each connected a midpoint of a side with a corner not on that side. (btw this is from your book: Pg. 242: 8.61) . . . a. Now, suppose that instead of the midpoint, our lines connect with a side at a point 1/3 of the way from the corner. What fraction of the area is shaded now? b. What if the lines connect ¼ of the way down the side? c. ** (extra) 1/nth of the way? x/3 2x/ 3 5. EFGH is a rectangle with EF = 12 and area 192. EGJI is a parallelogram such that H is on JI . What are the possible values for the area of EGJI? (Pg. 242: 8.64) € 6. 7. Find the length GF in the drawing below, given that BC = 9: (Pg. 242: 8.65) In trapezoid ABCD, AD || BC . m∠A = m∠D =45°. If AB = 6 and the area of ABCD is 30, find BC. (Pg. 243: 8.66) € 8. 9. The lengths indicated on the rectangle shown are in centimeters. What is the number of square centimeters in the area of the shaded region? BE SURE to justify your work (assumptions not ok) very carefully (Pg. 243: 8.68) P is inside rectangle ABCD. PA = 2, PB = 3, and PC = 10. Find PD. (Pg. 243: 8.69) ANSWERS: 1) 20 2) 8/3 3) 4) ¼ 16 160 a. b. 2/5 9/17 c. 1− 5) 6) 192 20 7) 8) 25 9) a. b. c. 2 2 95 2n (nsquared +1)
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