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Geo I Review for Semester 1 Quiz 10 Name ________________ Date ___________ Use quadrilateral QUAD for # 1 – 8. Q (-2, 1) U (2, 3) A (3, 1) D (-1, -1) 1. What is the most specific name for QUAD? Briefly describe (use actual WORDS) each of your steps. Step 1: Find the slopes of all 4 sides. This will allow me To determine if the quadrilateral is a trapezoid, some Kind of a parallelogram, or neither. I got slopes of 2/4 = ½ , -2/1, 2/4 = ½, and -2/1. 2 pairs of opposite sides tells me this is a parallelogram Step 2: Look at the slopes of a pair of consecutive sides to determine if they are perpendicular. This will tell me whether or not the parallelogram is a rectangle. 2/4 = ½ and -2/1 Opposite reciprocal slopes tell me that this IS a rectangle. Step 3: Check to see if it is also a rhombus by determining if the diagonals are perpendicular. I found the diagonals to have slopes of 0 and 4/3 The slopes are not opposite reciprocals of each other, so this is NOT a rhombus. The most specific name for the quadrilateral is a rectangle. 2. If QUAD is reflected over the y-axis, give the image points. Q’ (2, 1) U’ (-2, 3) A’(-3, 1) D’ (1, -1) 3. If QUAD rotated 180°, give the image points. Q’ (2, -1) U’ (-2, -3) A’(-3, -1) D’ (1, 1) 4. If QUAD is translated 3 units to the right, and 1 unit down, give the image points. Q’ (1, 0) U’ (5, 2) A’(6, 0) D’ (2, -2) Use quadrilateral QUAD for # 1 – 8. Q (-2, 1) U (2, 3) A (3, 1) D (-1, -1) 5. Find the length of QU. 42 + 22 = d2 From -2 to 2 is 4 spaces, from 1 to 3 is 2 spaces. The length of QU is the square root of 20. 6. Find the midpoint of UA (Average!) 3 + 2 = 5 5 / 2 = 2.5 1+3=4 (2.5, 2) 4/2=2 7. Find the length of the diagonal QA. 8. Find the midpoint of diagonal UD From -2 to 3 is 5 spaces, from 1 to 1 is 0 spaces. (Average!) -1 + 2 = 1 1 / 2 = .5 52 + 02 = d2 -1 + 3 = 2 The length of QU is the 5 2/2=1 (.5, 1) . For # 9 & 10, ΔABC = ΔDEF. 9. Which is the largest < in ΔABC? E A 2x + 3 B D (2x – 10)° 4x – 1 3x – 2 C 10. Which is the shortest side in ΔDEF? 6x – 6 F (x + 15)° B D A (x + 25)° (2x)° C F E 2x + 3 = 3x – 2 5=x DE =3(5) – 2 = 13 EF = 4(5) – 1 = 19 DF = 6(5) – 6 = 24 2x – 10 = x + 25 x = 35 m<A = 2(35) – 10 = 60 m<B = 35 + 15 = 50 m<C = 2(35) = 70 DF is the longest side, so E is the largest < in ΔDEF. (Flashlight) <B corresponds to <E, so <B is the smallest < in ΔABC, AC is the shortest side. (Flashlight) DF corresponds to AC, so <B is the largest < in ΔABC AC is the shortest side in ΔDEF C Complete the proof. 1 Given: BC // AD AB // CD B 4 Prove: BC = AD BC // AD AB // CD Given Given <1 = <3 <2 = <4 // lines alt int <s = // lines alt int <s = ∆ABC = ∆CDA ASA BC = AD CPCTC D 2 AC = AC Reflexive Prop 3 A