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7. Which of the following statements is TRUE? A. A trapezoid can have four equal sides. B. A trapezoid can have three right angles. C. The base angles of an isosceles trapezoid are congruent. D. The diagonals of an isosceles trapezoid bisect each other. 8. The base angle of an isosceles trapezoid measures 118", what is the measure of its opposite angle? A, 118" B. 180" C. 90" D. 62" 9. The diagonals of an isosceles trapezoid are represented by (2x - 47)cm and (x + 31)cm. What is the value of x? A. 37 B. 39 C. 78 D. 80 10. A cross section of a water trough is in the shape of a trapezoid with bases measuring 2 m and 6 m. What is the length of the median of a trapezoid? A. 2 m B. 4 m C. 5 m D. 8 m Performance Standard Assessment Directions: Illustrate the identified quadrilaterals then solve each problem with solution. 1. ABCD is a rhombus. What is the measure of ZDAB, If ZABC = 108"? 2. Paul built a four-sided wood frame in the shape of a parallelogram with vertices FACE. If mzA = 50" then find mzC. 3. Quadrilateral SOFT is an isosceles trapezoid with SO | | TF and EN as its median. If SO = 4x - 3, TF = 3x + 6 and EN = 12, how long is each base, 4. A quadrilateral kite has its vertices WIND with WI = IN and WD = ND. Find its area if one of the diagonals is 6" more than the other and WN + ID = 20". RUBRIC: Learning Task: Solves problems Involving Parallelogram, Rhombus and Trapezoid. Score 5 3 2 0 Criteria Solves the Solves the Solves Solves the Started to No problem problem the problem solve the attempt correctly correctly problem incorrectly problem with with with but failed complete incomplete partially to solution solution correct continue solution2, If maREC= 3x-2 and maICE= 2x+20, find the maICE Solution: m/REC= 3x-2 and Given mzICE = 2x+20 Since myREC = MZICE Base angles of isosceles trapezoid are congruent Therefore, we have: 3x-2 = 2x+20 3x-2+2 = 2x+20+2 Apply Addition Property of Equality by adding 2 3x = 2x+22 on both sides of the equation and simplify. 3x + (-2x) = 2x + (-2x) +22 Apply Addition Property of Equality by adding -2x * = 22 on both sides of the equation and simplify. The value of x is now equal to 22 MEICE # 2x+20 Substitute the value of x in 2x+20 and simplify to = 2(22) +20 get the mz ICE. = 44+20 MZICE = 64 The mZICE is now equal to 64. Answer: Therefore, mzICE= 64. 3.What is the value of x if meREC= x+21 and mzCIR= 2x-18? Solution: mREC = x+21 and Given meCIR = 2x-18 Since meREC+ Opposite angles of isosceles trapezoid are mZCIR=180 supplementary. Therefore, we have: x+21+ 2x-18 = 180 x+21+ 2x-18 = 180 Combined like terms and simplify. 3x+3 = 180 3x+3+ (-3) = 180 + (-3) Apply Addition Property of Equality by adding -3 3x = 177 on both sides of the equation and simplify. IGN = 177 G Apply Multiplication Property of Equality by multiplying - on both sides of the equation and x = 59 simplify. The value of x is now equal to 59. Answer: Therefore. & = 59. C. Consider the Kite REST with diagonals RS and ET that intersect at O. E 1. If RE= 3x and RT= 6x, find the value of x if the perimeter of the kite is 90cm. 2. If OR= 3x+5 and OS= 2x+15, find the R O S value of X. 3. If ET = 21 cm, RS=8 cm, ER= 10em, and RT= 17em, find the perimeter and area of the kite REST. TTheorems on Isosceles Trapezold Theorem 3: The base angles of an isosceles trapezoid are congruent. Theorem 4: Opposite angles of an isosceles trapezoid are supplementary, Theorem 5: The diagonals of an isosceles trapezoid are congruent. Theorem 3; The base angles of an isosceles trapezoid are congruent. Isosceles Trapezoid MATH ZHMA = ZTAM Theorem 4: Opposite angles of an isosceles trapezoid are supplementary. Isosceles Trapezoid LOVE 20 and ZE are supplementary