LATEST Geometry 100% SOLUTIONS REVISED 2023//2024

Figure ABCD is a parallelogram. What is the value of p? - ANSWER 6 Figure LMNO is a parallelogram. What is the value of x? - ANSWER 20 Figure CDEF is a parallelogram. Which measures are correct? Check all that apply. - ANSWER n = 10 CF = 59 FE = 42 Figure ABCD is a parallelogram. What are the measures of angles B and D? - ANSWER A. ∠B = 55°; ∠D = 55° Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees. What is the value of x? - ANSWER 20 Figure JKLM is a parallelogram. The measures of line segments MT and TK are shown. What is the value of y? - ANSWER 7 The parallelogram shown represents a map of the boundaries of a natural preserve. Walking trails run from points A to C and from points B to D. The measurements shown represent miles. What is the sum of the lengths of the two trails? - ANSWER 16 miles A plot of land is in the shape of a parallelogram with the dimensions shown. How many feet of fencing are needed to enclose the lot? - ANSWER 68 feet Figure ABCD is a parallelogram. What are the measures of angles B and C? - ANSWER B. ∠B = 65°; ∠C = 115° Figure ABCD is a parallelogram. What is the perimeter of ABCD? - ANSWER 44 unit What is the perimeter of parallelogram LMNO? - ANSWER 80 The perimeter of parallelogram ABCD is 46 inches. What is DA? - ANSWER 4 What is the measure of angle O in parallelogram LMNO? - ANSWER 105 In parallelogram ABCD, what is DC? - ANSWER 13 In parallelogram PQSR, what is PQ? - ANSWER 9 Given: AB ≅ CD and AD ≅ BC Prove: ABCD is a parallelogram. What is the missing reason in step 3? - ANSWER SSS congruency theorem In parallelogram LMNO, what are the values of x and y? - ANSWER x = 55, y = 14 What is the measure of angle L in parallelogram LMNO? m∠L = - ANSWER 40 Which best explains if quadrilateral WXYZ can be a parallelogram? - ANSWER WXYZ is not necessarily a parallelogram because it is unknown if WC = CY. Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a parallelogram. What is the missing reason in step 6? - ANSWER CPCTC Consider the diagram and proof below. Given: WXYZ is a parallelogram, ZX ≅ WY Prove: WXYZ is a rectangle What is the missing reason in Step 7? - ANSWER consecutive ∠s in a ▱ are supplementary A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal? - ANSWER 41 units Rectangle PQRS is shown with its diagonals, PR and QS. What type of triangle is △STR? - ANSWER isosceles triangle Figure ABCD is a parallelogram. If ABCD is also a rhombus, what must be the value of x? - ANSWER 13 What is the approximate side length of the square? - ANSWER 4.2 units Rhombus LMNO is shown with its diagonals. The length of LN is 28 centimeters. What is the length of LP? - ANSWER 14 ABCD is a square. What is the length of line segment DC? - ANSWER 13 A quilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side length of the rhombus. Which measures are true for the quilt piece? Check all that apply. - ANSWER a = 60° The perimeter of the rhombus is 16 inches. The length of the longer diagonal is approximately 7 inches. The figure shown is a rhombus. Which equation is true regarding the angles formed by the diagonals and sides of the rhombus? - ANSWER x + y = z The perimeter of the rectangle is 146 units. What is the length of the longer side? - ANSWER 45 units